School Science Lessons
UNPhysics1a Physics experiments
Colour, gas discharge tubes, light sources, reflection, refraction, sound, waves
Please send comments to: J.Elfick@uq.edu.au
2014-07-26
Table of contents
4.100 Colour
4.200 Light sources, producing light
4.300 Reflection of light at flat surfaces, plane mirrors
4.400 Refraction of light at curved surfaces, magnifiers

4.100 Colour
4.117 Absorption spectrum of sodium
4.132 Colours of sunlight, rainbow
4.137 Colours of soap films
4.138 Colours of oil films
4.139 Colours of transparent objects, colour filters
4.140 Colours of opaque objects
4.144 Colours of the blue sky and the sunset
4.145 Colours of the sea
4.114 Dispersion, spectrum with a ray box
4.133 Electromagnetic radiation
4.115 Emission spectrum
4.116 Incandescent lamp
4.135 Infrared rays source
4.143 Mix coloured lights
4.141 Mix coloured pigments, blue and yellow chalk
4.142 Rotate colour discs
4.134 Spectroscope, diffraction grating
4.136 Ultraviolet light source

4.200 Light sources, producing light
4.117 Absorption spectrum of sodium
4.103.1 Candoluminescence
4.115 Emission spectrum
38.8.3 Fluorescent lamp
4.116 Incandescent lamp
4.135 Infrared rays source
4.120 Light rays through lenses
4.105 Light travels in straight lines, pinhole magnifier
4.102 Low voltage light source
4.103 Luminescence
4.104 Luminance and illuminance, candela, candlepower, lumen, lux
4.103 Sources of light

4.300 Reflection of light at flat surfaces, plane mirrors
4.106 Reflection of beams of light
4.111 Laws of reflection using a ray box
4.109 Mirror images, (inversion, lateral inversion)
4.110 Ray box for beams of light
4.112 Reflection from a concave mirror with a ray box
4.113 Reflection from a convex surface
4.108 Reflection with a smoke box
4.107 Smoke box to study light rays

4.400 Refraction of light at curved surfaces, magnifiers
4.127 Critical angle and total internal reflection
4.120.1 Focal length of a convex lens
4.128 Image with a convex lens, magnifying glass
4.120 Light rays through lenses
4.129 Magnifying power of a lens
4.129.1 Magnifiers, magnifying glass
4.125 Measure refractive index
4.131 Optical bench to study lenses
4.121 Refraction in a smoke box
4.122 Refraction in water illusions, pool depth, bent stick, rising coin
4.123 Refractive index using real depth and apparent depth
4.124 Refractive index using real depth and apparent depth, air to liquid
4.126 Refraction from air to water
4.130 Water drop magnifier, water lens

23.3.0 Solid expansion
23.3.01 Thermal shock
23.3.02 Fluid expansion
23.3.1 Expanding solid when heated
23.3.3 Expansion gauge
23.3.5 Thermostat
23.3.7 Shrink fit
23.3.8 Bar breaker, the force of contraction
23.3.9 Bend glass by expansion
23.3.10 Trevelyan rocker
23.3.11 Expanding quartz and glass
23.3.12 Expansion tube
23.3.13 Expanding wire, sagging wire
23.3.15 Motor car flashing lights
23.3.16 Compensated balance wheel of a watch
23.4.2 Reaction of sodium in liquid oxygen
23.4.6 Heat water in a sealed flask
4.102 Low voltage light source
See diagram 28.199: Low voltage light source
Make a compact light source from any small, high intensity electric light bulb that has a short, straight filament, e.g. light bulbs used in car tail lamps. Use a small light source to make very sharp shadows with the light bulb filament end on. Cover the light source with a small drink-can. Darken the room. Punch 2 mm diameter holes in the drink-can on all sides. Blow smoke around the can to make the emerging rays visible. Make enough holes so that you can see clearly where the light comes from and in what direction it travels.

4.103 Luminescence
See 35.16 Luminescence, (Geology)
Luminescence is emission of light for any reason other than a rise in temperature, e.g. excited photons returning to a ground state. Chemiluminescence is luminescence resulting from a chemical change. However, the term phosphorescence is also used to describe a situation when the luminescence persists even though the exciting cause has been removed. Luminescence that does not persist when the exciting cause is removed is called fluorescence, e.g. a fluorescent light.
4.103.1 Candoluminescence
Candoluminescenceis the light from heating substances with a flame to a high temperature so that some wavelengths are more than expected by blackbody emission at that temperature. This occurs in some transition metals and rare earth metal oxides, e.g. zinc oxide, cerium oxide, thorium dioxide.
Carl Auer, later Freiherr von Welsbach, 1858-1929, Austria, invented the Welsbach gas mantle containing thorium nitrate and cerium nitrate to increase light from gas lamps. Gas mantles are pieces of fabric soaked in metal oxides. They were used for gas lighting in homes, but nowadays are used only for gas pressure lamps for outdoors work and camping.

4.104 Luminance and illuminance, candela, candlepower, lumen, lux
See 6.3.1.7: Luminous intensity, candela, cp
Luminous intensity, C, is a measure of the brightness of a light source, i.e. how much light emitted per second, and is measured in the candela, cd, formerly candle power. Luminance, L, measures the brightness of a surface in candela per square metre. A source of light measuring one candela emits one lumen of light, 1 lm.
Illuminance, or illumination, I, is a measure of the quantity of light falling on a surface at a distance from the light source, and is measured in lux, lx. Illuminance is directly proportional to luminous intensity, C, and inversely proportional to the square of the distance, d, from the light source, so I = C / d2, One lux is the illumination of one lumen per square metre. One lux is the brightness at one metre from 1 candela light source. Light meters, exposure meters, used in photography, measure illuminance in the unit lux.
Experiment
See diagram 28.10.11: Projected Filament with Lens, thin lenses Turn on the light bulb. Move the light bulb to focus the image on the side wall. The focal lengths are marked on the lenses. Show the effect of aperture size on the sharpness on the focus by placing different sized stops in front of the lens.

4.105 Light travels in straight lines, pinhole magnifier
See diagram 28.105.1: Light travels in straight lines | See diagram 28.105.2: Pinhole camera | See diagram 4.105.2: Pinhole camera (no labels) | See diagram 28.105.3: Shadows | See diagram 4.105.3: Shadows (no labels)
1. Make a pinhole magnifier. Cut a very small hole through a piece of cardboard with a pin. Hold the cardboard very close to the eye in good light and look through the hole at some small print. The print appears larger and clearer because light rays pass through the small hole then spread out. The small hole functions like a camera shutter keeping out the extra light that would make the image blurred.
2. Look down on a tightly closed fist. Open the fist very slightly to let the smallest amount of light pass through. Look at some fine print through the fist. Move the fist up and down to get the best magnification.
3. Pierce a hole with the pin in the centre of a piece of cardboard. Hold it 10 cm in front of one eye. Hold the pin between the card and the eye. See an upside down image of the pin will be observed.
4. Make a pinhole in a sheet of aluminium foil. Hold the aluminium foil between a lighted candle and the wall. See the inverted image of the candle flame on the wall.
5. Hold the hole in the cardboard 3 cm from the eye. Keep the eyelid almost closed. See inverted images of the eyelashes. All objects will cast an upside down image on the retina when the eye is focussed on them. The brain interprets the upside down image as right side up.
6. Make a pinhole in the middle of one end of a rectangular box, e.g. a shoe box. Cut a window in the other end of the box and use adhesive tape to attach over it a screen made of greaseproof paper, lunch wrap paper, baking paper. Draw the letter T on a piece of thin white paper, or greaseproof paper using a marker pen. Attach the paper with the T drawn on it to the front of a light source. In a dark room, direct light from the light source towards the pinhole and, at the other end of the box, look at the image on the screen. The image of the T is inverted.

4.106 Reflection of beams of light
See diagram 28.106.1: Reflections | See diagram 28.106.2: Laws of reflection
Reflections: A Light source, B Comb, C Mirror
Laws of reflection: D Reflection in a plane mirror, E Eye, F Angle of incidence, G Angle of reflection
Laws of reflection: 1. The incident ray, reflected ray and the perpendicular normal, N, at the point of incidence all lie in the same plane. 2. The angle of incidence, i, = the angle of reflection, r.
Hold a comb so that the sun's rays shine through the teeth and fall on a piece of white cardboard laid flat on a table. Tilt the cardboard so that the beams of light are several centimetres long. Place a mirror held upright diagonally in the path. Note that the beams which strike the mirror reflect at the same angle. Turn the mirror and note the direction of reflected beams.

4.107 Smoke box to study light rays
See diagram 28.202: Smoke box to study light rays | See diagram 4.107: Ray tracing
A Smoke box, B Electric torch, about 1 metre from the smoke box, C Smoke, D Light beams, E White card
Make a wooden box 30 cm wide and 60 cm in length. Fit clear plastic or glass in the top and front of the box. Leave the back open and cover with a black cloth curtain. Hang this curtain in two sections, with a 10 cm overlap at the centre of the box. Paint the inside the box with black paint. Cut a window 10 cm high and 5 cm wide midway between the top and bottom of one end and 10 cm from the glass front. This window lets in light rays. You can cover the window with different kinds of openings cut from cardboard and fastened with drawing pins. Fix a piece of black cardboard with a 5 mm diameter hole over the window. Fill the box with smoke from a lighted incense stick or smouldering paper. Remove the smoke source and allow the apparatus to stand for 5 minutes to clear the smoke box of the heavier particles. The interior of the smoke box appears clear but still contains enough fine smoke particles to produce visible scattering of light rays.
Set up an electric torch or a projector 1 metre from the window. Focus the light down to a parallel beam and direct it at the holes in the window. The smoke makes the light rays in the box visible. Also, a laser may be mounted on a labjack and raised or lowered as required, or the light may be passed through a series of slides to produce multiple beams. Use the smoke box for ray tracing through optical elements, e.g. lenses, mirrors and prisms.

4.108 Reflection with a smoke box
See diagram 28.203: Reflection with a smoke box
A Reflected beam of light, B Mirror, C Light beam
Fill the smoke box with smoke. Shine the torch beam on the hole in the window. Hold a plane mirror inside the box and note the clearly defined rays after reflection from the mirror. The light rays reflect without scattering. Move the mirror to change the angle of reflection.

4.109 Mirror images, (inversion, lateral inversion)
See diagram 28.109.1: Lateral inversion | See diagram 28.204: Inversion
1. Write a name on a sheet of paper with a black pencil. Hold the paper up to the light with the writing away from you. Look at it with a mirror.
2. Write a name on a piece of carbon paper, carbon side up. Then read the underside of the sheet of paper. Look at it with a mirror.
3. Wear a heavily-printed T-shirt inside out. Look at yourself in the mirror.
4. Write a name on a piece of paper, but look at what you are writing on the paper only through a mirror. Some people can write in mirror images without using a mirror.
5. Look at the letters b, d, p, in a mirror, at the side of the letters, above or below the letters. What do the letters now read? Write a secret message in mirror writing.
6. Place a photograph of your face on the bench. Imagine a line that cuts the image of your face from top to bottom and exactly in half. Place a mirror vertically on the photograph with the back of the mirror on the imaginary line and the front of the mirror facing to the left. Move your head slightly to the left so that you can see your whole face, half the face from the photograph and half the face reflected in the mirror. Note whether you face is symmetrical and whether this composite image is the same as in the photograph.
7. Make an artificial mirror image. Fold a sheet of paper in half and paint a shape on one half. Fold the other half over the painted half and press down. Open the folded paper to see the mirror images.
8. Paint a design on the right side of your face. Look in a vertical mirror and notice that the design is on the left side of the face in the mirror. Place another vertical mirror so that its edge is touching the first mirror at an angle of about 120o. Position yourself so that you can see half your face in the first one mirror and the other half of your face in the second in the other mirror. The painted design is now on the right side of your face in the mirror.
9. Draw a 6-pointed star on a square piece of paper so that the points of the star almost touch the edges of the paper. Draw a second star 2 cm inside the first star. The area between the two stars is your star path. Place a barrier, e.g. a book, between you and the sheet of paper so that you cannot see the star path on the paper, but you can look over the book. Place a vertical mirror on the other side of the paper so that you can see the star path in the mirror. Hold a pencil vertically down on the star path. Move the
pencil around the star path until you come back to where you started. Note how long it takes you to move your pencil around the star path without running off it.
4.110 Ray box for beams of light
See diagram 28.205: Ray box | See diagram 4.110: Ray box: A Ray box, B Lamp C Lens, D Screens
This apparatus consists of two sides of an oblong box 22 × 6 cm with the lens placed at one end of the box. The box has no bottom, and in use rests on paper pinned to cardboard. The light source is a 12 V 24 watts, W, motor car lamp. The lamp holder has a sleeve of brass tubing just fitting into a hole in a wooden slide, which forms the top of the box. The groove in front of the lens is for screens and filters. A piece of card with a slit in it provides narrow rays, and a hair comb will give a bundle of rays. Adjust the position of the slider to form convergent, parallel or divergent beams. Do experiments with light rays using plane mirrors, glass blocks and prisms. A curved piece of tin will show a caustic curve. In experiments with lenses and in refraction, push down the lamp so that the light does not pass over the top of the obstacle. For optical experiments, in front of the lens use a card with a hole and cross wires.

4.111 Laws of reflection using a ray box
See diagram 28.206: Laws of reflection with a ray box | See diagram 4.111: Reflection with a ray box
A Laws of reflection with a ray box, B Lamp, C Lens, D Cork, E Mirror
Cut a vertical groove in a cork and fix a plane mirror in it by cutting a groove in the cork. Stand the mirror on the table. Place a piece of drawing paper in front of the mirror. Insert a board with a vertical slit in a ray box to make light rays travel along the paper surface and reach the mirror. Shine beams of light from the ray box along the paper and mark the path of the incident ray and the reflected ray with crosses. Join the crosses and continue the lines to the mirror. Remove the mirror. Draw the normal line at the intersection of
the above two lines. Measure the angle of incidence and the angle of reflection to see whether they equal.

4.112 Reflection from a concave mirror with a ray box
See diagram 28.207: Reflection from a concave mirror | See diagram 4.112: Reflection from a concave mirror
A Lamp, B Lens, C Concave mirror
Make a concave mirror from a fruit tin cut in half or a part of a metal ring. Measure the focal length of the mirror by directing a parallel beam of light on to it.

4.113 Reflection from a convex surface
See diagram 28.208: Reflection from a convex surface | See diagram 4.113: Reflection from a convex surface
A Convex mirror, B Lens, C Lamp
Use a convex mirror, e.g. a motor car wing mirror, side mirror, with the ray box and note the reflected rays of light. Compare its reflection with the reflection from a plane mirror and a concave mirror. In motor vehicles in Australia, Canada, India and USA, "Objects in the mirror are closer than they appear" is on the passenger side mirror because these convex mirrors makes objects appear smaller, e.g. another car behind in an adjacent lane. So the message is a warning against changing lane without warning.

4.114 Dispersion, spectrum with a ray box
See diagram 28.114: Dispersion with a triangular prism
See diagram 4.114: Dispersion with a triangular prism: A Normal, B White light, C Red, D violet
Dispersion occurs when light of different wavelengths is spread out by a prism into a spectrum
1. Use a glass prism to produce a spectrum from a parallel beam of light. Place a card with a narrow slit in front of the lens of a ray box. Use colour filters to suppress certain colours, e.g. use a transparent purple filter so that you see only red and blue lines on the screen.
2. Study light rays through a prism. Hold a glass prism in a parallel beam of light and note how the beam refracts. Rotate the prism on its axis. When white light splits into the colours of the spectrum, i.e. disperses, the violet light end of the spectrum refracts more than the red light. The refractive index of violet light is greater than the refractive index of red light. However, monochromatic light has only one colour and does not disperse.

4.115 Emission spectrum
If individual atoms of an element receive enough energy, they produce a characteristic line emission spectrum. Each element emits characteristic lines of radiation with specific wavelengths. Compounds contain more than one kind of atom, so they produce a band emission spectrum.

4.116 Incandescent lamp
Light bulb IEC Light Source 2 Wires 2.5V MES, "Scientrific" (commercial website)
Hot solids or liquids emit wavelengths of radiation depending on the temperature as a continuous spectrum. At lower temperatures they emit red wavelengths, so the metal appears to be "red hot". At higher temperatures, they emit the full visible spectrum as white light, so the metal appears to be "white hot" or "incandescent". The incandescent filament in an electric light globe, a filament lamp, is "white hot".

4.117 Absorption spectrum of sodium
See diagram 28.133: Incandescent spectrum | See diagram 4.117: Absorption spectrum of sodium
1. When white light passes through a vapour of atoms, they absorb their characteristic wavelengths of light and reduce these wavelengths in the continuous spectrum emitted to produce a line absorption spectrum. White light from the sun travels through cooler elements surrounding it that absorb their characteristic wavelengths. The dark absorption lines in this line absorption spectrum, i.e. solar spectrum, identifies these elements, e.g. Helium.
2. Heat a wire coated in sodium chloride in a Bunsen burner flame and placed in front of a sodium light source. The sodium vapour from the heated wire appears as a black mist because of its absorption of the characteristic wavelengths of sodium.

4.120 Light rays through lenses
See diagram 28.120: Ray diagrams for lenses | See diagram 4.120: Ray diagrams to show the formation of images by lenses
A Real, inverted, diminished image, B Real, inverted same size image, C Real, inverted, magnified image, D Virtual, erect, magnified image, E Concave lens, virtual, erect, diminished image
Parallel rays of light that pass through a convex lens, converging lens, all pass through the principle focus, F. Parallel rays of light that pass through a concave, diverging lens, diverge as if coming from the principle focus, F. In the diagram, 1. to 4 are convex lenses that form real images when the object is more than one focal length from the lens.
1. Light rays come from a distant object,
2. The object is twice the focal length from the lens,
3. The object is between the focal length and twice the focal length from the lens,
4. The object is less than the focal length from the lens,
5. A concave always produces the same kind of image.
Experiment
1. Take the lenses from an old pair of spectacles or used optical instruments, or purchase reading glass lenses and hand magnifiers. Cover the window of a smoke box with a piece of black cardboard with three holes punched in a vertical line. The holes should be the same distance apart, but the distance between the two outside holes should be a little less than the diameter of the lens. Arrange a torch supply parallel to light rays. Fill the box with smoke and hold a double convex lens in the path of the three beams of light so that the middle beam strikes the centre of the lens. Note the beams on the opposite side of the lens from the source of light. Repeat the experiment using a double concave lens.

4.120.1 Focal length of a convex lens
1. Attach a sheet of white paper on a wall opposite a bright window with the sun not visible because it is behind an outside object, e.g. a tree. The light rays passing through the window from the distant sun will be almost parallel. Hold a convex lens vertically about 5 cm from the paper the move it in a straight line towards the window until a clear image of the window appears on the white paper at a distance of the focal length of the lens.

4.121 Refraction in a smoke box
See diagram 28.212: Refraction in a smoke box | See diagram 4.121: Refraction in a smoke box
A Bottle of water, B Electric torch, C Light beam, D Refracted ray
1. Fasten a piece of black cardboard with a single hole in it 8 mm square over the window of the smoke box. Arrange a torch to shine a beam of light into the box. Fill a large, preferably rectangular, bottle with water and add a few drops of milk or a pinch of starch or flour to make the water cloudy. Cork the bottle. Fill the box with smoke. Hold the bottle at right angles to the beam of light and note the direction of the light through the water. Tilt the bottle at different angles to the beam of light and note how the path of light through the bottle changes.
2. Refraction is the change in direction of light as it crosses a boundary from one optical medium, e.g. glass, into another medium, e.g. air. Light bends towards the normal when entering a medium that is optically more dense. Light bends away from the normal when entering an optically less dense medium. Light paths are reversible for refraction. The incident ray, refracted ray, and normal to the boundary at the point of incidence, all lie in the same plane.

4.122 Refraction in water illusions, pool depth, bent stick, rising coin
See diagram 28.122.3: Rising coin | See diagram 4.122.3: Rising coin: 1. You can see A but not B, 2. You can see A and B as A1 and B1, 3. Air, 4. Water
See diagram 28.122.1: Stones in a swimming pool | See diagram 28.122.2: Bent stick
1. Drop three stones, (P1, P2, P3) in a flat bottom swimming pool. Drop P1 below you, P2 farther away and P3 at the far side. Look at the three stones from a position directly above P1. P1 appears to be at the greatest depth, P2 at lesser depth and P3 at still lesser depth. The bottom of the swimming pool filled with water appears curved when viewed from above. If the refractive index of water = 1.33, the apparent depth of the swimming pool looking straight down, normal view, = true depth / 1.33 = 3 /4 × true depth.
2. Place a stick in a tall container of water, so that part of the stick is above the surface. Note where the stick enters the water. The stick appears bent because the light rays refract as they pass from water to air. The image of each point on the stick below the water forms above its real position because of refraction at the air / water interface.
3. Put a coin in a non-transparent, short and thick cup on the table. Stand away, and arrange your line of vision so that you can just see a point A on the far side of the coin. Your view of the coin is almost shut out by the wall of the cup. Keep the position of your head unchanged while pouring water into the cup without moving the coin. As you pour in the water, the coin appears to rise, so you can now see the entire coin. The positions of A1 and B1 are the intersection of the backwards extensions of the refracted ray and the
ray from A or B that is vertical to the surface of water and not refracted. The refracted ray from A is parallel to the refracted ray from B.
4. More than half fill a tall transparent glass with water. Insert a pencil so that the side of the pencil touches the right hand top of the glass and the lower end touches the left inner wall of the glass, but not the bottom. While looking down into the water, see the lower end of the pencil touching the wall and at the same time move your left finger from up and down along the wall of the glass until you think the finger points to the lower end of the pencil. Look through the side of the glass to see the actual position of the pencil. It is under your left finger. The position of the left finger is the position of the image of the end of the pencil.

4.123 Refractive index using real depth and apparent depth
See diagram 28.123: Real depth and apparent depth of glass
Place a block of glass on the table. Place a pin close to the side of the glass at O. The head of the pin may be seen from point A, at the edge of the glass opposite O. Place an inverted drawing pin at B on the glass. Adjust the position of B so that its point, coincides with the image of the pin at A seen through the glass. Measure the lengths of OA and A2. The plane CD with point A is the refraction plane of light, the refractive index from air into glass = AO / A2.
4.124 Refractive index using real depth and apparent depth, air to liquid
See diagram 28.124: Real depth and apparent depth of water is the curving of light around edge object and consequent spreading when it passes through a narrow gap. A single slit diffraction pattern differs from double slit interference.
1. Observe a vertical filament lamp slit formed by holding two finger together and looking through the narrow gap between the fingers.
2. Attach a pin at O to the bottom of a beaker with Plasticine (modelling clay). Place the beaker on the white paper on the table. Pour water into the beaker without disturbing the pin at O. Look down to see the image I of the pin at O through the liquid surface. Horizontally clamp another pin S to a stand near the beaker. Adjust the stand to make S at the same height as I. Mark the position of S on the outside of the beaker. Pour off the water in the beaker without disturbing the pin at O. Measure OL and IL, where L is a point on the surface of the water. Repeat the experiment with different heights of water. Calculate the reflective index from air into water = OL / IL.

4.125 Measure refractive index
Snell's law: sin i / sin r = n, a constant called the refractive index
Substance and refractive index (for liquids at 20oC): diamond 2.4173, flint glass 1.655, crown glass 1.517, ethanol 1.361, water 1.33299, carbon dioxide 1.00450, air 1.000293 vacuum 1.0
See diagram 4.125.1: Refraction: 1. Eye, 2. Torch, 3. Screen, 4. Incident ray, 5. Emergent ray
See diagram 4.125.2: Refractive index: A Incident ray, B Refracted ray, C Air, D Glass
See diagram 4.125.3: Pin against face of a glass slab: A Pin, B Pointer, C Slab
See diagram 28.125.1: Refraction | See diagram 28.125.2: Refractive index | See diagram 4.125.2: Refractive index (no labels)
1. Attach a black paper collar to the front of an electric torch. Prepare a screen with a 1 cm diameter hole, or use a CD-ROM disc as a screen. Hold the screen in front of the electric torch to limit the light beam to a narrow, horizontal beam. Put a rectangular container, e.g. a fish tank or transparent plastic box, on a sheet of white paper on the table. Draw a line on the white paper at right angles to the middle of the container, the normal. Draw another line at 45o to the first line. Fill the container with saltwater and add
drops or milk or fluorescein. Direct a beam of light along the 45o line into the container, the incident ray. Note the path of the beam of light through the water. Use smoke or chalk dust scattered in the air to make the beam of light visible in the air before entering and after leaving the container. Look through the end of the container, looking along the ray, to see that it is straight. The angle between the normal and the incident ray is the angle of incidence, i. The angle between the normal and the path of the light beam through the water is the angle of refraction, r. Refractive index = sin i / sin r. The beam of light leaving the container, after passing through the water, is the emergent ray. The incident ray and the emergent ray are parallel so there is lateral displacement between them. Lateral displacement depends on the breadth of the container, the angle of incidence and the refractive index of the air and the solution in the container.
2. Repeat the experiment by putting a rectangular slab of glass, or a rectangular plastic box contained full of a transparent solution, on white paper on the table. Draw the outline of the slab on the white paper. Place a pin, X. at the middle of the nearest side of the slab. Draw a line through X at 45o to the side of the slab. Look along the line and put two pins, A and B, on the line and two pins, C and D, in line with A and B on the opposite side of the slab. Put a pin, Y, where a line through DC meets the slab. Remove the slab and draw the normal at X (X1 to X2) and the normal at Y (Y1 to Y2). The path of the light ray is ABXYCD. Use a protractor to measure the angle of incidence AXX1 and the angle of refraction X2XY. Calculate the refractive index, sin AXX1 / sin X2XY. Check that AXX1 = DYY1, and X2XY = Y2YX. If refractive index of glass = 1.5, a glass slab viewed from the normal appears to be 1 / 1.5 = 2 / 3 of its true thickness.
3. Substance and refractive index (for liquids at 20oC): diamond 4.4173, flint glass 1.655, crown glass 1.517, ethanol 1.361, water 1.33299, carbon dioxide 1.00450, air 1.000293.
3. Put a pin against the far face of a glass slab. Hold a pointer down over the slab and move it until it is above the image of the pin, as seen through the slab. If the true thickness of the slab = T, and the apparent thickness = AT, i.e. the distance of the pointer from the front of the slab, then refractive index = T / TA.

4.126 Refraction from air to water
See diagram 28.215: Refraction in milky water | See diagram 4.126: Refraction in milky water
Pour a few drops of milk into a glass of water to cloud the water. Punch a small hole in a piece of dark paper or cardboard. Place the glass in direct sunlight, and hold the card upright in front of the glass so that a beam of sunlight shines through the hole. First hold the card so that the hole is just below the water level. Note the direction of the beam in the water. Then raise the card until the beam strikes the surface of the water. Note the direction of the beam of light and experiment to find out how the angle at which the beam strikes the water affects the direction of the beam in the water.
4.127 Critical angle and total internal reflection
See diagram 28.127.1: Candle behind fish tank | See diagram 28.127.2: Spoon in glass of water
See diagram 28.216: "Pouring light"
Critical angle is the angle of incidence in a more dense medium, which produces an angle of refraction of 90o in a less dense medium. Total internal reflection occurs when the critical angle of incidence is exceeded. Triangular prisms can change direction of light by total internal reflection if the angle of incidence > critical angle.
When a parallel beam of light from the lamp is aimed vertically upwards from beneath the cylindrical clear plastic trough containing water the beam is not deviated. It passes straight up.
If the beam is aimed up at a small angle of incidence, i, then both an internally reflected beam, R, and a refracted beam, T, can be seen. The beam, T, is passing from water to air, from a medium of higher optical density to lower optical density, so the refraction is away from the normal, angle r > angle i.
As the angle of incidence, i, is increased, r increases until the direction of the transmitted beam, T, approaches the direction of the surface of the water. When i reaches the critical angle the refracted ray just grazes the surface of the water, so angle of refraction becomes 90o. When i > critical angle there is no refracted beam because all the light is reflected as total internal reflection. There is a sudden increase in the intensity of the reflected beam as the angle of incidence increases beyond the critical angle. The critical angle is an angle of incidence in an optically more dense medium, which produces an angle of refraction of 90o in a less dense medium. When the critical angle of incidence is exceeded, there is no refracted light at all. Instead, all the light is totally internally reflected.

Experiments
1. See diagram 28.127: Semicircular Plexiglas
Rotate a semicircular slab of Plexiglas with the light ray entering the exiting through the curved surface. Rotate the semicircular slab until the critical angle is reached and total internal reflection is obtained.
2. Put a short lighted candle behind a glass or plastic rectangular fish tank. Fill the fish tank with water to a level just above the wick. Look at right angles to the fish tank so that you can see the lighted candle directly opposite. Raise and lower the level of your eye above and below the level of the water. The top of the candle flame and the bottom of the candle flame around the wick are in one line. Move your head to the left parallel to the front glass of the fish tank. When your eye is above the water level, the top of the flame appears to move to the left. When your eye is below the water level, the bottom of the flame appear to move to the left. The angle between a line from the candle at right angles to the fish tank, the normal, and your line of sight, the incident ray, is increasing. For most glass, when this angle reaches about 43o, the critical angle, the incident ray cannot pass into the water, so the image disappears.
3. Return to the first position where you first looked at the candle directly opposite you. Lower your eye to the level of the bottom of the fish tank and look up at the bottom of the water surface. See the reflection of the lower part of the candle that you saw when your eye was just below the level of the water. Light from the candle up to the surface of the water is at an angle greater than the critical angle is reflected at the water surface, total internal reflection.
4. Stand a spoon in a glass of water at the edge of the table. Look up from just below the table surface at the spoon pointing down towards you. The surface of the water acts like a mirror and so you see the reflection of the lower part of the spoon that is under water. However, you cannot see the upper part of the spoon above water.
5. "Pour" light from a drink-can. Remove the top of a drink-can. Punch a hole in the side of the drink near the bottom and close the hole with a stopper. Pour water into the drink-can until it is three quarters full. Put the drink-can next to a sink in a dark room. Hold an electric torch vertically down in the top of the drink-can so all the light shines down into the water. Remove the stopper and let the water pour into the sink. The light from the electric torch appears to pour out with the water. Most of the light cannot escape from the falling water because the critical angle is exceeded and it reflects off the water surface by total internal reflection. This principle is used for "light pipes", fibre optic cables and decorations using light shining up through a bunch of tubes.
6. Shine a light into one of the two sides of a right angle reflecting prism. The light reflects off the hypotenuse and passes out through the other side. The light reflects because the angle of incidence at the hypotenuse is greater that the critical angle for crown glass, 43o. Reflecting prisms are used in binoculars, prismatic compasses and periscopes. Prisms allow you to see around corners!

4.128 Image with a convex lens
See diagram 28.217: Image with a magnifying glass
Darken all the windows in a room but one. Hold a convex lens (hand lens, magnifying glass) in the window and direct it at the scene outside. Bring a piece of white paper slowly near the lens until the image picture forms. Note the position of the image.

4.129 Magnifying power of a lens
See diagram 28.218: Magnifying power of a lens
Use a magnifying glass to get a clear image of the lines in an exercise book. Adjust the distance of the magnifying glass so that a line seen through the magnifying glass coincides with a line seen outside the magnifying glass. Compare the number of spaces seen outside the lens with a single space seen through the lens. The lens shown in the diagram magnifies three times. Linear magnification is the ratio of the size (height) of the image to that of the object or the image distance to the object distance. Magnification is the measure of enlargement or reduction of an object in an imaging optical system, e.g. X100. In astronomy it is the factor by which an image produced by an optical device increases the angular size of an object where magnification of a telescope = focal length of the telescope / focal length of the eyepiece.
4.129.1 Magnifiers, magnifying glass
Magnifier, X 2.5, "Scientrific", (commercial website) | Magnifier, on stand, "Scientrific", (commercial website) |
Magnifier, with lamp, "Scientrific", (commercial website) |
Magnifying glass, glass lens, magnification × 3, 75 mm diameter
Magnifying glass, bifocal, plastic lens, magnification 2 × and 6 ×, 75 mm diameter
Magnifying lens, hand lens, folded magnifier, magnification 10 ×

4.130 Water drop magnifier, lens
See diagram 28.1.17: Water lens. paper clip
1. Roll the end of a copper wire around a thick nail to make a loop. Cut the wire to leave a handle. Dip the loop in water then take it out so that the water in the loop is the shape of a convex lens. Look at the loop from the side to see the shape of the convex lens with the centre thicker than the edges. Use the water lens to look at a line in the palm of your hand. Move the lens towards and away from your hand to see the line become upright then inverted.
2. Very gently knock the loop so that the meniscus breaks then reforms to form a new water lens in the shape of a concave lens. Look at the loop from the side to see the shape of the concave lens with the centre thinner than the edges. Use the water lens to look at lines in the palm of your hand. Move the lens backwards and forwards.
3. Put a drop of water on a piece of clean glass. Observe the lines in the palm of your hand again. The drop of water acts as a magnifier.
4. Use needle nose pliers to bend the end of a "slide on" paper clip to form a loop. Dip the loop into a beaker of water then tap it against the side of the beaker to form a water lens inside the loop. The water lens could be a convex lens (widest in the middle) or a concave lens (thinnest in the middle). Examine the letter "e" with your water lens. Note whether the lens is a convex lens or concave lens. Dry the loop and try to make the other kind of lens.

4.131 Optical bench to study lenses
See diagram 28.219: Optical bench | See diagram 4.131: Optical bench: A screen B lens C light source D metre stick E blocks
An optical bench allows you to hold mirrors and lenses in position and to measure distances accurately with a metre scale. Use wooden or plastic blocks with grooves that just fit over the metre scale. Stick a pin into the centre of each block. Use strips of tin screwed to the side of the blocks to make lens holders. Attach a torch bulb to a block as a light source.

4.132 Colours of sunlight, rainbow
See diagram 28.220: Colours of sunlight
P30 Glass Prism, equilateral prism, rainbow spectrum,, "Prof Bunsen", (commercial website)
As the light passes from the air into the water droplet, it is refracted. White light is made of a wavelengths ranging from 400 to 700 nm. The index of refraction (n) is inversely proportional to the wavelength. Hence the index of refraction for the red wavelength (700
nm) is lower than the index of refraction for the violet wavelength (400 nm). Red light is bent less than the violet wavelength or the red light travels faster than the violet wavelength.
Experiments
1. Simple spectrum. Pass white light, W, through a slit, S, then a lens, L, to obtain a pure spectrum on a screen, R, red to V, violet. N is the normal.
2. Darken a room into which the sun is shining. Drill a hole on a piece of thick cardboard. Cover the window of a room with a dark curtain, but leave a space for the piece of cardboard. Make sure that only one beam of light shines through the hole in the cardboard into the room. Hold a triangular glass prism in the beam of light so that it passes through the prism then reaches the opposite wall. Observe the coloured spectrum of sunlight produced through the prism on the opposite white wall.
3. Make the sunlight spectrum with a glass cup. Put a round glass cup without handle and colour on a windowsill. Fill it with water. Place a piece of white paper on the floor near the windowsill. Lift the cup so that you may see a rainbow or spectrum on the paper.
4.135 Infrared rays source
See diagram 28.223: Infrared rays: A Heat lamp, B Visible light, C Iodine solution, D Infrared rays, E Burning black paper.
See diagram 4.135.1: Spectrum pic | See diagram 4.135.2: IR Spectrum pic (University of Melbourne)
1. Iodine dissolved in alcohol gives a filter transmitting in the IR but absorbing in the visible. To produce infrared radiation, use a heat lamp for treating muscular ailments. Fix the infrared lamp on the table so that it shines horizontally on the bulb of a large flask of water. The flask acts as a lens. Hold your hand between the lamp and the flask to feel the heat. Move a piece of black paper on the other side of the flask to find the focal point. Add iodine solution to the water and shake the flask to make the iodine solution uniform. Place the flask back at the original position. Hold a piece of cotton wool soaked in methylated spirit at the focal point. It starts to burn. Iodine solution stops visible light but allows the longer infrared wavelengths to pass through. Infrared radiation is invisible electromagnetic radiation of wavelength between about 0.7 micrometers, (0.7 m), and 1 millimetre, (1 mm), i.e. between the limit of the red end of the visible spectrum and the shortest microwaves. All objects above 0 K, including humans, absorb and radiate infrared radiation. Infrared radiation is used in medical photography and treatment, in astronomy and in photography in fog. Infrared radiation can be detected by a Golay cell detector that contains xenon gas.
2. Show that electromagnetic radiation extends beyond the visible into the infrared and its equivalence with heat radiation. A normal colour spectrum is produced with the aid of the slit and slide projector and the prism. Rotating the prism will bring different sections of the spectrum into the entrance pupil of the thermopile. Maximum reading is obtained just passed the red end of the spectrum. This experiment requires that the infrared filter is removed from the slide projector. Plastic slides will melt.
3. Set up a slide projector to display a normal spectrum on the screen. Remove the IR filter and place a 2-3 mm slit in the slide carriage. Focus a digital movie camera on the image and compare the images in normal mode and night vision mode. The CCD elements are sensitive to the infra red and normally an IR filter is used to block the IR. In night vision mode this filter is swung out of the way, allowing the infra red to be displayed.

4.136 Ultraviolet light source
See diagram 28.224: Ultraviolet light source
1. Attach two lamp holders to insulating material and fasten it to the bottom of a cardboard carton with the top removed. Fix two argon lamps into the lamp holders and connect the lamps in parallel without leaving any bare wire exposed. Cut a notch in the side or end of the box for the electrical lead cord. Invert the box cut a peephole to allow viewing without direct eye exposure to the ultraviolet light. Ultraviolet light may cause serious damage to the eyes. However, you can observe different objects in "black light" by placing the cardboard box over the objects, turning on the switch to the power source and observing the objects through the peep hole. Objects that glow under ultraviolet light include clothing dyed with fluorescent dyes, e.g. socks and ties, soap powders containing an "optical brightener", e.g. "Bluo", and white clothes washed in these powders, fluorescent paints and lacquers, fluorescent chalk, some minerals, e.g. willemite, fluorites, opals and sphalerites.
2. Use an argon lamp as an ultraviolet light source to display fluorescence. Mount an argon lamp in a light proof box and cut a peephole in the box for viewing. Be careful! Avoid direct eye exposure to the ultraviolet light, which may damage the eyes. To note different objects in black light, put the box over the objects and turn on the argon lamp. Clothes may contain fluorescent dyes, e.g. bright socks. Ultraviolet rays in ordinary sunlight cause fluorescent dye to glow. Soap powders may contain a brightener. White clothes washed in these powders fluoresce in the ultraviolet radiation from the sun or from an argon light bulb. Fluorescent paints, lacquers and chalk are also available. Some minerals fluoresce in ultraviolet light, e.g. ilmenite, opal, sphalerite and some fluorites.
3. Collect objects that glow under ultraviolet light. Ultraviolet light is used for bank note testing, in hospitals and in fluorescent watches. Ultraviolet radiation is light rays invisible to the human eye, of wavelengths from about 4 × 10-7 to 5 × 10-9 metres, where the X-ray range begins. Ultraviolet radiation causes sunburn and the formation of vitamin D in the skin. Ultraviolet rays are strongly germicidal and may be produced artificially by mercury vapour lamps for therapeutic use. The radiation may be detected with ordinary photographic plates or films.

4.137 Colours of soap films
Make a strong soap solution as used for blowing soap bubbles. Fill a flat dish with the solution then dip a cup into the solution until a soap film forms across the cup. Hold this in a strong light so that the light reflects from the film. Note the colours. Tilt the cup to make the film vertical, and note the changes in the colour pattern as the film becomes thinner towards the top. The colours seen in thin films come from the interference of the light waves reflected from the front and the back of the film.

4.138 Colours of oil films
1. Add black ink to a flat dish filled with water. Put the dish in a window where light from the sky is very bright but not in direct sunlight. Look into the water so that light from the sky reflects to your eye. While looking at the water, place a drop of oil on the nearest surface at the edge of the dish. Note a brilliant rainbow of colours flashing away from you towards the opposite edge. Blow on the surface to see a change in the colours. Interference of white light results in spectral coloured fringes.
2. Add two drops of clear nail varnish to a bowl of water. Dip black paper in the water and leave it to dry. Look at the paper in sunlight from different angles and see the rainbows form as light is dispersed by the layers of nail varnish.

4.139 Colours of transparent objects, colour filters
See diagram 28.227: Colour filters
Study colour filters. Observe the coloured light that passes through a transparent object and the colour of the transparent object. Prepare some transparent objects with different colours, e.g. coloured glass, coloured cellophane. Roll a cylinder with a piece of white paper and fix it vertically above a piece of white paper on the table. Put the transparent objects on the cylinder under sunlight or white light so that light shines down through the transparent object. Observe the colour of the paper on the table and compare it with the colour of the transparent object. The colours are the same. Transparent objects absorb some colours and some colours to pass through them. They have colour because of the colours they transmit and that they absorb all other colours. Water has high transparency. It absorbs some light in the infrared and ultraviolet regions of the spectrum but transmits the visible radiation necessary for photosynthesis. The colour of a transparent object is a mixture of those wavelengths that it transmits. The colour of an opaque object has a colour due to the mixture of wavelengths it reflects, the others being absorbed. The diffused light is the colour of light that the object absorbs less. The nature of the surface of an object can affect the direct reflection of different coloured light. If the ratio of reflection to certain colour light is greater than that of other colour light, the object may appear the colour of this colour light. A white opaque body, or a colourless transparent body reflects or transmits all wavelengths in the same proportion as they occur in white light. A polished silver surface may reflect 93% of the white light incident upon it and white paper may reflect 80%, depending on the nature of the surface and the angle of incidence.

4.140 Colours of opaque objects
1. Note the colour of a piece of red cloth in white light or sunlight. In a dark room, note the colour of the same piece of red cloth in red, blue, green, and yellow. The red cloth appears black unless placed in light of the same colour or in white light or sunlight. Opaque objects have colour because of the light they reflect. In white light or sunlight they absorb the other colours of the spectrum. Repeat the experiment with a piece of white cloth. White objects may reflect any colour. Repeat the experiment with a piece of
black cloth. Black objects absorb all colours and do not reflect any colour. Repeat the experiment with coloured illustrations from a magazine. In white light or sunlight, remember the colour of each part, e.g. red flowers and green leaves, then compare its colour under the coloured light.
2. Note the colour of dry sand. Add water to the sand and note any change of colour. Dry sand is composed of pieces of quartz that reflect light in all directions so that the sand appears almost white. When sand is wet, the layer of water on each quartz grain reflects back some light at the air water surface, so the sand appears darker in colour.

4.141 Mix coloured pigments, blue and yellow chalk
Use a piece of blue chalk and a piece of yellow chalk. Crush them and mix them evenly. The mixture will be green. The green here is not pure. It is between the colour of yellow and green in the spectrum. The colour of yellow absorbs all colours except yellow and green. The colour of blue absorbs all colours except blue and green. So only yellow, blue and green are reflected. However, the yellow and blue absorb each other, so the light reflected into your eyes is only the green colour. Mixed pigments reflect the
common colour for all the pigments in the mixture and subtract all the other colours. Repeat the experiment with water colours with the same density.

4.142 Rotate colour discs
Newton's colour wheel, "Scientrific", "Scientrific", (commercial website)
See diagram 28.230: Rotate colour discs
1. Mix coloured lights by using water colours painted on discs of cardboard. Paint a yellow "egg yolk" on one side of a 10 cm disc, and a blue "yolk" on the other side. Suspend the disc between loops of string. Twist the loops then pull outwards to make the disc spin. The resulting colour is nearly white.
2. Paint radial segments alternately red and green. Note the resulting mixture of red and green lights reflected to the eye by spinning the disc on a string.
3. Divide a white disc into seven segments. Paint each segment with one of the seven colours of the visible spectrum, (violet, indigo, blue, green, yellow, orange, red). Spin the disc rapidly, e.g. attached to an electric motor. The disc appears nearly white, depending on the purity of the colours. This disc is called Newton's disc or Newton's colour wheel.

4.143 Mix coloured lights
Shine red, blue and green lights on a white screen so that the colours overlap. Red overlaps with blue to produce magenta. Blue overlaps with green to produce turquoise, blue-green. Green overlaps with red to produce yellow. In the centre, red, blue and green overlap to produce white, so red, blue and green are called the primary colours. Magenta, turquoise and yellow are called the secondary colours. For colour photography, each primary colour is processed separately by its layer of light sensitive emulsion. For
colour television, the primary colours are separated by the camera and added together again in the television set. The "primary colours" of an artist are red, blue and yellow, not red, blue and green, because artists use pigments, not coloured lights.

4.144 Colours of the blue sky and the sunset
See diagram 28.144: Colours of the blue sky and the sunset
When light passes through the atmosphere more of the shorter waves from the blue end of the spectrum are scattered by gas molecules in the air and small dust particles than the longer waves from the red end of the spectrum. So the blue light scatters in all directions and the sky appears blue in all directions. So the light from a low sun at sunrise and sunset contains mostly waves from the red end of the spectrum. During the day, not much light is scattered light from a high sun.
Experiments
1. Observe ripples of water passing through upright reeds and note that shorter wavelength ripple are scattered more by passing through the reeds than longer wavelength ripples.
2. Shine a narrow beam of light through a fish tank or a large beaker filled with water. Add drops of milk or powdered milk or acidified sodium thiosulfate solution while stirring until you can see the beam shining through the water. Look at the beam both from the side and from the end, where the beam shines out of the container. Viewed from the side, the beam appears blue. Viewed parallel to the direction of the beam, the beam appears orange-red or yellow. See the colour of the beam change from blue-white to orange-yellow along the length of the beam. Let the light project onto a white card at the end of the tank. The beam spreads so it is not so narrow as at the source of light. Particles in the milk scatter the light and so allow you can see the beam from the side. Blue light is scattered much more than orange light or red light, so we see more blue light from the side. Orange light and red light are scattered less so we see them at the end. The shorter wavelength blue light has a greater refractive index so it bends more than longer wavelength red light with a smaller refractive index. Similarly, atmospheric gases smaller than one wavelength scatter blue light, so the sky appears blue. This phenomenon is called Rayleigh scattering. The sun is white hot but it appears orange-red because the white light from it has lost some blue light. When the sun is on the horizon, its light takes a longer path through the atmosphere to your eyes than when directly overhead. So at sunset most of the blue light is lost by scattering leaving the orange-red light, i.e. white light minus blue light. Only the longer wavelengths reach the eyes. If there were no scattering, and all the light from the sun travelled straight to the earth, if not looking at the sun, the sky would look dark as it does at night. Large particles, e.g. dust, smoke, and pollen, scatter light without breaking white light into component colours. This is called Mie scattering. It is the cause of the whiteness of clouds, mist,
milk, latex paint and the white glare around the sun and moon during a mist. The sun has the same colour as a black body at 5780 K.
3. Place a lens from Polaroid sunglasses between the light source and the fish tank. Hold the lens vertically and turn it while another person observes the beam from above and another person observes the beam from the side. When the person above observes a bright beam, the person at the side observes a dim beam, and vice versa. This is the same effect when look through two parallel sun glass lenses and you turn one of the lenses. At a certain position no light, or very little light, passes through both lenses. So the scattering in the fish tank polarizes the light. Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light. Electromagnetic light waves from the sun or an electric lamp come from electric charges vibrating in many directions perpendicular to the direction of the light beam. Sunglasses include a Polaroid material that absorbs light vibrating horizontally and so reduces glare. So the light reaching your eyes is polarized light.

4.145 Colours of the sea
The sea appears blue because it absorbs all of the wavelengths of sunlight except the short blue wavelength. The oxygen content of water molecules absorbs the red end of the spectrum. Blue light is scattered in water in all directions to cause the blue oceans. Similarly at the North and South polar regions the ice and icebergs appear blue. The blue colour changes if the sea contains phytoplankton, suspended sediments, and dissolved organic chemicals as in the seas in the temperate regions.

23.3.0 Solid expansion
H10 Bimetallic Jumping Disc, different thermal expansion of metals, "Prof Bunsen", (commercial website)
Expansion due to heat, thermal expansion, expansivity, coefficient of expansion
Most bodies increase their volume upon heating under normal pressure. Solids retain their shape during temperature variations so you distinguish between linear expansion, area expansion and volume expansion (cubic expansion). Applications of solid expansion include shrink fitting, rivetting, expansion gap, expansion roller, bimetallic strip, fire alarm, thermostat
Linear expansion
The length of a solid changes with temperature. The fraction by which the length at 0oC to changes per oC is called the coefficient of linear expansion. For example, for Aluminium, α = 23 × 10-6, but most tables just show Aluminium = 23, Copper 16.7, Iron 11.8, Glass 8.5. If a solid at temperature t1 has length L1 has expanded at temperature t2 to length L2, then L2 =L1 [1 + α (t2 - t1)] or L = Lo (1 + α  T), where α = the coefficient of linear expansion.
Surface expansion (superficial expansion, area expansion)
Similarly A2 = A1 [1 + 2 α (t2 -t1)] or A = Ao (1+2 α T)
α A = 1 / A × dA / dT, where A = area and dA / dT is the rate of change of that area per unit change in temperature
Surface expansion has been likened to expansion of a photographic print
Cubic expansion
and V2 = V1 [1 + 3 α ([t2 - t1)] The coefficient of cubic expansion for a solid, is about three times the coefficient of linear expansion. {A cube of edge 1 cm at 0oC and volume 1 cc would become a cube of edge (1+ α ) cm at 1oC, so its volume would become (1 + α )3 = (1 + 3x +3x2 + α3 ) cc. However, for solids, α is very small, so x2 and x3 are negligible, hence the formula V2 = V1 [1 + 3 α ([t2 - t1)]}

23.3.01 Thermal shock
Thermal shock is differential expansion where at some place or places on a material stress expansion causes a crack to form and the structure to fail. Thermal shock can often be avoided by changing temperature more slowly. A thermal shock can occur by spraying a liquid on an alight light bulb or lava lamp.
23.3.02 Fluid expansion
All of the above formula are applicable only if α has a small value and do not apply to substances ß where α changes with temperature.
When a volume change with temperature occurs, the fraction by which the volume at 0oC changes per oC is called the coefficient of volume change, e.g. mercury = 180 × 10-6, air = 3400 × 10-6. Liquids generally increase in volume as the temperature increases and have coefficients of cubic expansion about 10 times that of solids. Water is an exception, because as you heat water from 0oC it contracts rather than expands. At 4oC, water occupies its smallest volume, i.e. it has the highest density. Water obeys the general laws of thermal expansion except in the temperature interval from 0oC to 4oC. The cubic expansion formula does not apply to expansion of gases because all gases expand by 1/273 of their volume at 0oC as in Charles' law. So for expansion of gases you must use Charles' law - the volume of an ideal gas at constant pressure is directly proportional to the absolute temperature. Air and most other gases at atmospheric pressure have a coefficient of cubic expansion of 0.0034 (oC)-1.

23.3.1 Expanding solid when heated
See diagram 23.106: Expansion of solid
A = copper tubing, B = clamp, C = bicycle spoke roller, D = straw
1. To show and compare thermal expansion of different metals. The expansion apparatus consists of a cast iron base with two vertical supports that hold the metal expansion rod. The pointer is zeroed by the adjusting screw illustrated and the burners lighted beneath the rod. Use aluminium, brass, copper and mild steel expansion rods. Expansion of the rod causes deflection of the pointer and this deflection may be compared for the different metals for the same time interval.
2. Use a 2 metre piece of stout copper tubing. Put it on a table and fix one end by a clamp. Underneath the other end put a bicycle spoke to act as a roller. A drinking straw fixed to the roller by wax will show any movement of the rod resting on it. Blow steadily down the tube between the fixed end and the middle. This arrangement detects the expansion of the tube caused by the hot breath. Pass steam through the tube, and note the motion of the pointer. Repeat the experiment with different types of tubing.
3. Heat a 60 cm copper rod for five minutes with a Bunsen burner. Note the movement of the pointer. The rod rests on a knitting needle so when the rod moves it rolls the needle. If the expanding rod caused the needle to do one complete turn of 360 degrees the hot copper rod has expanded a distance equal to the circumference of the knitting needle.
23.3.3 Expansion gauge
See diagram 23.4.10: Expansion gauge
Engineers use expansion gauges to check whether metal parts are no larger than a certain size.

23.3.5 Thermostat
Bimetallic strip, "Scientrific", (commercial website)
See 4.5.0 Thermostat, (Bimetallic strip), (Experiments)
A small bimetallic strip acts as a switch in a thermostat. Bimetallic strip bends away from an electrical contact when heated to turn off a light.

23.3.7 Shrink fit
Heat a brass ring and slip it onto a slightly tapered steel bar.

23.3.8 Bar breaker, the force of contraction
1. Heat an iron bar then tighten it in a yoke so it breaks a cast iron bar when the bar cools.
2. Bar breaker. Construct a strong iron bar so that it rests in two yokes on a cast iron base. Pin the bar on one end by a thin cast iron pin, and thread it on the other end so that it can be tightened. Heat the bar with the the gas jets located directly beneath the bar. Tighten the bar as it is heated. After the bar is fully tightened, dowse it with water. As the bar contracts the forces present are large enough to snap the cast iron pin. There is a delay between initial cooling and fracture of up to 30 seconds.

23.3.9 Bend glass by expansion
Heat one edge of a strip of plate glass with a Bunsen burner to cause the glass to bend towards the cooler side.

23.3.10 Trevelyan rocker
The Trevelyan rocker is a brass or copper bar and an extension. The brass bar has an S-shaped cross-section so that the bottom surface has two parallel knife edges. Heat the rocker and place the brass bar on a cold lead block with the end of the extension resting on the bench. The rocker starts to vibrate due to the rapid expansion of the lead causing the rocker to tip from edge to edge and emit a musical note. Press on the rocker with a pencil point to change the pitch of the note. The action is related to other rockers, e.g. the "celt" or rattle back.

23.3.11 Expanding quartz and glass
Heat both quartz and glass tubes with a high temperature torch and plunge into water. Heat a piece of quartz tube and quench it in water Try the same thing with Pyrex and soft glass.

23.3.12 Expansion tube
Pass steam through an aluminium tube with a dial indicator to show the change in length. One end of a tube rests on a needle attached to a pointer that moves as the tube is heated.

23.3.13 Expanding wire, sagging wire
Heat a length of nichrome wire electrically and watch it sag. Heat electrically a long iron wire or nichrome wire with a small weight hanging at the midpoint and see it sag. Pass one end of a heated wire is passed over a pulley to a weight. The pulley has a pointer attached.

23.3.15 Motor car flashing lights
Blinking lights on cars use a small unit containing is a bimetallic strip that heats up as current flows through it. The strip bends and opens the circuit. On cooling, the strip straightens and closes the circuit. You can adjust the timing of the cycle with a screwdriver.

23.3.16 Compensated balance wheel of a watch
See diagram 23.107: Compensated balance wheel of a watch
Examine the compensated balance wheel in a watch. As the temperature rises, the radius arm of the balance wheel expands to increase the moment of inertia about the axis and increase the period. The increasing temperature also reduces the elasticity of the hair spring to also increases the period. To compensate for these effects, the balance wheel is made of two strips of dissimilar metals fastened together, bimetallic strips, so that the metal with the smaller coefficient of expansion is on the inner side of the bimetallic strip. When the temperature increases, the radius of curvature of the bimetallic strip decreases because of the lesser increase in length of the inside strip and P and Q are fixed so R and S move in towards the axis, the moment of inertia of the balance wheel is lessened and the corresponding decrease in period compensates exactly for the increase in period caused by the change in elasticity.

23.4.2 Reaction of sodium in liquid oxygen
Drop a piece of potassium cooled in liquid oxygen into water.

23.4.6 Heat water in a sealed flask
See diagram 23.4.6: Heat water in a sealed flask
1. Fill the flask of some cold water of height 1-2 cm. Seal the mouth of the flask with a one hole rubber stopper. Insert a straight capillary through the stopper so that the lower end of the capillary enters the water and is about 1-2 mm from the bottom of the flask. The upper end of the capillary remains outside the flask. Heat the coloured water in the beaker to the temperature of 80oC more. Place the flask into the hot water in the beaker to heat the water in the flask to 70oC. During heating, tightly press the mouth of the flask with your hand to seal the air in the flask. After 2 minutes, suddenly take your hand off the mouth of the flask and observe a stream of water spurting out of the upper end of the capillary tube.
2. Place a wet coin on the upper end of the capillary tube. It will move up and down gently to produce some vibration sound. When you heated the air in the flask, its volume did not increase because you sealed the flask with your hand. So the air pressure increased and a stream of water current spurted out of the upper end of the capillary tube when you take your hand off the mouth of the flask.