School Science Lessons
Physics - Optics, reflection, refraction
Updated: 2008-03-29
Please send comments to: J.Elfick@uq.edu.au
See also: Interesting websites
Table of contents
Lasers and laser hazards 2.13
4.103 Sources of light
4.104 Luminance and illuminance
4.105 Light travels in straight lines, pinhole magnifier
4.114 Study the spectrum with a ray box
4.115 Emission spectrum
4.116 Incandescent lamp
4.117 Absorption spectrum
4.118 Fluorescent lamp
4.119 Diffraction of light
4.120 Light rays through lenses
4.142.1 Measure solar ultraviolet radiation
28.1.0 Geometrical optics, speed of light
28.2.0 Reflection from flat surfaces
28.3.0 Reflection from curved surfaces
28.4.0 Refractive index
28.5.0 Refraction at flat surfaces
28.6.0 Total internal reflection
28.8.0 Thin lens
28.9.0 Pinhole camera
28.10.0 Thick lens
28.11.0 Optical devices
28.1.0 Geometrical optics, light rays and shadows, speed of light
2.210 Diffraction of light
28.1.1 Light rays,  visible light, polarized light, speed of light, rectilinear propagation,  path of light
1.9 Light and shadow game (Primary)
1.10 Spinning picture (Primary)
1.11 Mirror game (Primary)
5.10 How light travels (Primary)
28.2.0 Reflection from flat surfaces
28.2.01 How light travels
28.2.02 Laws of reflection
28.2.03 Reversibility of light
28.2.04 Real images and virtual images
28.2.05 Plane mirror images
28.2.06 Lens images
28.2.07 Image equation
28.2.08 Reflection values of different substances
4.106 Reflecting beams of light
4.107 Make a smoke box to study light rays
4.108 Reflection with a smoke box
4.109 Mirror images
4.110 Make a ray box for beams of light
4.111 Laws of reflection with a ray box
4.112 Reflection from a concave mirror with a ray box
4.113 Reflection from a convex surface
28.2.2 Reflection of light by a plane mirror
28.2.3 Angle of incidence and angle of reflection
28.2.4 Reflection, reversibility of path of light
28.2.5 Make a periscope
28.2.6 Reflection with two projectors
28.2.8 Laws of reflection with an electric torch
28.2.9 Mirror image needs a flat smooth surface
28.2.10 Image position in a plane mirror, pin parallax method to locate image
28.2.11 Reversed writing, identify a person's handwriting, lateral inversion
28.2.13 Clock face in two mirrors
28.2.14 Plane mirror
28.2.15 Angle of incidence reflection
28.2.16 Diffuse reflection
28.2.17 Scattering with aluminium foil
28.2.18 Reflection normal and grazing
28.2.19 Corner cube, corner reflector
28.2.20 Mirrors at an angle
28.2.21 Parallel mirrors
28.2.22 Candle in a glass of water
28.2.23 Location of image
1.11 Mirror game (primary)
5.11 Mirror reflects light (primary)
28.3.0 Reflection from curved surfaces
4.89 Reflection at a straight barrier
4.90 Reflection at a curved barrier
28.3.1 Spherical mirrors
28.3.2 Concave and convex mirrors
28.3.4 Reflection from a concave mirror (converging mirror)
28.3.5 Reflection from a convex mirror (diverging mirror)
28.3.6 Spherical aberration in a mirror
28.3.7 Variable curved mirrors
28.3.8 Mirror and rose, flower in a vase
28.3.9 Cold candle
28.3.10 Amusement park mirrors
28.3.11 Energy at a focal point
28.4.0 Refractive index
28.4.01 Methods to find refractive index
28.4.1 Refractive index of ice
28.4.2 Disappearing eye dropper
28.4.3 Refraction with shadow and cube
28.4.4 Mesh on wall
28.4.5 Abbe refractometer
28.4.6 Mirage
28.5.0 Refraction at flat surfaces
4.86 Make a ripple tank
4.87 Circular pulses
4.88 Straight pulses
4.91 Refraction of waves
4.92 Diffraction in a ripple tank
4.121 Refraction in a smoke box
4.122 Refraction in water
4.123 Refractive index using real depth and apparent depth
4.124 Refractive index using real depth and apparent depth, air to liquid
4.125 Measure refractive index
4.126 Refraction from air to water
4.127 Critical angle and total internal reflection, "pouring" light
4.128 Image with a convex lens, magnifying glass
4.129 Magnifying power of a lens
4.130 Water lens
4.131 Optical bench to study lenses
28.1.3 Refracting telescope, Galileo telescope
28.5.2 Refraction tank, ripple tank, aquarium
28.5.3 Refraction model
28.5.4 Coin in a cup
28.5.5 Light in a tank
28.5.6 Stick in water, bent stick
28.5.7 Acrylic / lead glass refraction
28.5.8 Minimum angle of deviation, minimum deviation of a prism
28.5.9 Refraction of light, air to water, in air
28.6.0 Total internal reflection
28.6.1 Optical disc with prism semicircle
28.6.2 Critical angle in ripple tank, refraction tank, aquarium
28.6.3 Critical angle and total internal reflection
28.6.5 Light below surface
28.6.6 Water / benzol surface
28.6.7 Black ball turns silver
28.6.8 Diamond
28.6.9 Right angle prism inverter
28.8.0 Thin lens
28.8.1 Convex lens forms an image
28.8.3 Concave lens, focal length of concave lens using lens formula
28.8.4 Ripple tank convex lens, concave lens
28.8.5 Ray tracing with lenses
28.8.6 Thin lens projection
28.8.7 Real image formation
28.8.8 Projected arrow with lens
28.8.9 Thin concave lens
28.8.10 Effect of medium on focal length
28.8.11 Pinholes projected with lens
28.8.12 Curvature of a lens, spherometer
3.7 Burn with a magnifier (Primary)
5.12 Images with a lens (Primary)
5.13 Water drop magnifier (Primary)
28.9.0 Pinhole camera
28.9.3 Fish-eye camera
5.14 Pinhole camera (Primary)
28.10.0 Thick lens
28.10.1 Depth of focus
28.10.2 Chromatic aberration
28.10.3 Barrel and pincushion distortion
28.10.4 Off axis distortion
28.10.5 Astigmatism
28.10.7 Fillable air lenses
28.10.8 Spherical lens
28.10.9 Wine bottle lens
28.10.10 Watch glass lens
28.11.0 Optical devices
28.11.1 Simple magnifier
28.11.2 Water drop magnifier
28.11.3 Model refracting telescope
28.11.4 Projector for filmstrips or slides
28.11.5 Microprojector
28.11.6 Use a microscope us a microprojector
28.1.1 Light rays,  visible light, polarized light, speed of light, rectilinear propagation,  path of light
Visible light is part of the electromagnetic radiation spectrum made up of (increasing frequencies, decreasing wavelengths) radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Light is a form of electromagnetic radiation that a physical change can produce, such as the heating of an object, or a chemical change, such as the burning of magnesium. An electromagnetic wave is a transverse wave, it can be polarized, it arises from accelerating charges and travels only at 3 X 108 m / sec. in a vacuum. The wave has a changing electric field and a changing magnetic field at 90o to each other.
Polarized light has the changing electric field component in one plane. Polarizers, e.g. as in Polaroid sun glasses, allow only one plane of changing electric field to pass through them
Speed of light in a vacuum (universal constant) c = 2.99792458 X 108 m / sec, to three significant figures: c = 3.00 X 108 m / sec. In transparent materials the speed of light is less than it is in a vacuum. Light travels in straight lines and causes shadows when an object is placed in the path of the light. Diffuse reflection of light occurs at surfaces that are not flat. Specular reflection occurs at polished surfaces.
Rectilinear propagation of light, shadows from point source and spotlight 
Path difference method
Method with a fast pulsar and fast oscilloscope. Insert different media in the path.
Rotating mirrors
A laser beam is used with the rotating mirror method.
Straight line propagation
Use a light in a vacuum. Place a flashing light in the bell jar to highlight the point. A good point source shows straight line propagation of light by shadow projection.
Propagation star
An intense radiation point source limited by a star-shaped aperture melts a star-shaped pattern on a paraffin backed black foil.
28.1.3 Refracting telescope, Galileo telescope
See diagram 28.1.3
Use two convex lenses, one with long focus and slightly thick diameter, another with short focus and slightly thin diameter. Hold each lens opposite to some object afar. Place a piece of white paper behind each lens to find the clearest image of the object on the paper. Record the approximate value of each focus. Use hard cardboard to roll two cylinders with nearly equal diameters and fix a lens on each cylinder, the length of each cylinder 2-3 cm longer than the focus of its lens. The fixing methods: use a piece of hard cardboard to roll two cylinders that can enclose their lenses; control the cylinders with thread or rubber tape then glue the cracks on their insides and outsides with white adhesive plaster. Glue a circle of hard cardboard strip at 0.5-1 cm from the rim of the slightly thick cylinder; place the long focus lens as the objective lens at the left of the hardboard strip. Then glue another circle of hard cardboard strip at the left of the lens so that the lens is fixed between two circles of hard cardboard strips. Like this, fix the short focus lens at the slightly thin cylinder as the eyepiece. At another end of the slightly thick cylinder cut a 3 mm x 1-2 cm quadrate window whose longer sides are horizontal; at the opposite side cut another same window, making sure that the focal plane of its lens is located at some axis section between the two windows. Like this, cut two same windows with the above at another end of the slightly thin cylinder. Insert the thin cylinder into another one and screw the thin one to make the two pairs of windows just opposite. Separately insert two M3 screws through the inside of the cylinders and gently screw two nuts on the outside. Let the objective lens face some object afar with then gently move the thin cylinder horizontally. You may see a clear image of the object when the two focal planes coincide. Here a contracted, inverted, real image of an object afar forms at the focal plane of the objective lens and the real image forms an amplified virtual image infinite far from the eyepiece. The amplification of this magnifying glass is the ratio of the focal length of the objective to that of the eyepiece.
28.2.01 How light travels
Plane mirror, ripple tank reflection diffuse reflection, location of real and virtual images in mirrors using ray boxes and ray tracing, properties of images, mirror image, lateral inversion, laws of reflection, characteristics of images formed by plane mirrors including: (a) a general mirror equation relating object distance, u, image distance, v, and focal length, f, applied with suitable conventions 1 / v + 1 / u = 1 / f, a qualitative and quantitative treatment of magnification, ray diagrams to show image formation with plane mirrors
Light travels in straight lines causing shadows when barriers much larger than the wavelength of light are placed in the path of the light. A full shadow is called the umbra and partial shadow is called the penumbra. On a sunny day observe the shadow of a tall vertical pole, e.g. a flag pole. At its base the shadow has sharp edges because it is umbra and no penumbra. The shadow of further up the pole has less and less sharp edges with more and more penumbra and less umbra.
28.2.02 Laws of reflection
The incident ray, reflected ray, and normal (perpendicular) at the point of incidence on the reflecting surface, all lie in the same plane.
The angle of incidence, i, is equal to the angle of reflection, r. These laws apply to both plane and curved reflecting surfaces.
28.2.03 Reversibility of light
If light can travel along one path via reflections, travelling along the reverse path must be possible for it.
28.2.04 Real images and virtual images
Image is a picture or appearance of a real object, formed by light that passes through a lens or is reflected from a mirror. A real image is one through which rays of light actually pass, and the image can form on a screen,  e.g. images produced by a camera or projector lens can be projected onto a screen. An image than cannot be projected onto a screen, such as that seen in a flat mirror, is known as a virtual image. A virtual image is an image from which diverging rays of light appear to come.
28.2.05 Plane mirror images
A mirror forms an image by the law of reflection. The focal length of a mirror depends only on geometrical considerations because the properties of the material do not affect the focal length when light reflects from a mirror surface. Images in a plane mirror are always virtual, upright, and the same size as the object, i.e. virtual, erect and not magnified. Any image in a plane mirror is as far behind the mirror as the object is in front of it so any point on the image, e.g. A', appears to be the same distance behind the mirror surface as the corresponding point on the object, A, is in front of the mirror surface.
28.2.06 Lens images
For the lens, the image forming properties depends on refraction through the lens material thus the focal length will depend both on geometric factors and the index of refraction of material of the lens.
28.2.07 Image equation
For both lenses and mirrors, the image and object distances are related by the same equation: u-1+ v-1= f-1, or 1 / v + 1 / u = 1 / f, where u is the distance from the object to the optical centre of the lens or to the mirror pole viz. object distance, v is the distance from the image to the optical centre of the lens or to the mirror pole viz. image distance, f is the focal length of the lens, which is positive for converging lenses and negative for diverging lenses.
28.2.08 Reflection values of different substances
Reflection values for 300 nm radiation: (1 = complete reflection) snow 0.85, dry sand 0.17, water 0.05, grass 0.025
28.2.2 Reflection of light by a plane mirror
See diagram 28.2.2
Put a piece of white paper on a table in  the sunlight.  Hold a black plastic hair comb teeth down on a table. Let light shine through the spaces between the teeth of the comb then onto the table to form a shadow of black and white stripes. Incline the paper to make the stripes on the paper become longer. Hold a vertically mirror on the table at an angle to the comb. The white stripes are reflected beams of light after going through the space between the teeth. Measure the angle between the incident beams of light and reflected beams of light. Turn the mirror and observe how the reflected beams of light turn.
28.2.3 Angle of incidence and angle of reflection
Push the pins into two rectangles of cardboard to make two optical sights as shown. Put a sheet of paper under the mirror. Put one sight, in front of the mirror, on the left side pointing in towards the centre. On the right side, line up the other sight so that the images of the four pins are all in line. Before you remove the mirror, trace along its back edge in contact with the paper. Press the optical sights down gently so that the ends of the pins leave a mark on the paper. Remove mirror and optical sights. Draw a line through the marks in the paper from the first sight, onto the mirror, and a line from the mirror through the second sight. Where these two lines meet on the surface of the mirror draw a line at right angles to the surface of the mirror, called the normal. Use a protractor to measure the angle of incidence and the angle of reflection.
28.2.4 Reflection, reversibility of path of light
See diagram 28.3.0
Surfaces that are not flat cause diffuse reflection of light. Polished surfaces cause specular reflection so that the angle of the incident ray to the normal at the point of reflection is equal to the angle of reflection for heat, light, radio waves and sound waves.
28.2.5 Make a periscope
See diagram 28.2.5
Use a strong tube or make a long box. Paint the inside black. Insert two small mirrors, parallel and at 45o angle to the tube.
28.2.8 Laws of reflection with an electric torch
See diagram 28.3.3
Use a 23 cm x 42 cm, flat, hard piece of cardboard. At 2.5 cm from the longer side of the cardboard draw a semicircle of radius 200 mm and equally divide the central angle. Bisect the semicircle at 90o line into two 1 / 4 circles. At the bottom of one 1 / 4 circle, remove the remained 2.5 cm wide strip. At the bottom of the other 1 / 4 circle, bend the 20 mm level line ahead. To bend it into right angle, cut it to the half deep beforehand. Glue the two 1 / 4 circles behind them with adhesive tape, along the 90o line and joining the 0o line and 180o line, leaving a very narrow slit at the connecting to rotate the 1 / 4 circle removed the 2.5 cm wide strip free. On the 20 mm wide strip place small plane mirror under the centre to make this 1 / 4 circle stand vertically in front of the mirror. Rotate another one backward then let it stay at some place. Cover the glass of a torch flashlight with a piece of black paper with a small hole in the centre. Let the light rays from the electric torch shine along the line with an arrow and reach the mirror at the centre. Rotate the back 1 / 4 circle to look for the reflected ray and measure the angle of incidence and the angle of reflection.
28.2.9 Mirror image needs a flat smooth surface
Put a piece of black paper on the table. On it put a flat-bottom glass container, e.g. a fish tank, containing water. Hold a pencil above the surface of the water. Note the image of the pencil. Put your finger into the water and move it up and down rapidly to form waves on the surface of water. Now you cannot see the image of the pencil. When surface of water becomes stationary and smooth again, the image reappears. Slightly crumple aluminium foil to produce an irregular surface. You cannot see the image of the pencil on that surface. Remove the black paper below the glass and observe whether the image of  the white holder or black holder is more clear. A clear image is produced by a smooth surface that can fully reflect the light rays. A rough surface cannot be used as a mirror.
28.2.10 Image position in a plane mirror, pin parallax method to locate image
See diagram 28.4.3
Cover a large white paper on the table, Stand up a plane mirror in centre of the paper by the method in 28.3.2 Draw a black point S on the paper in left front of the mirror by a pen. Put a projector on the paper in right front of the mirror, point at the black point in the mirror in two different directions in turn, after point it at each time press the pin to leave traces A1, B1, A2, B2 which meet at point S'. Connect SS' and original position line of the mirror MN to point 0. Measure the length of SO and S'O and the angle between SS' and MN. Finally conclude the law of the image in the plane mirror.
28.2.11 Reversed writing, identify a person's handwriting, lateral inversion
See diagram 4.109.1: Lateral inversion |  See diagram  4.109.2:  Inversion
Place a piece of carbon paper with two sides on a table and a piece of white paper on it. Vertically stand a plane mirror near some outside of the white paper. Ask other person to write a familiar word then you read the word through the mirror without seeing the word on the paper directly. You may fell very difficult to read and even not tell what the word is. Invert the paper to make the back of the paper upwards then you read the word duplicated. You may feel difficult similarly. Move the mirror to the next side of the paper then you read the word through the mirror. You will identify the word instantly.
28.2.13 Clock face in two mirrors
See diagram 28.4.6
Observe the image of an object in place that two mirrors meet with their edges touching at right angle. Stand two mirrors of square shape on the table with their edges across to right angle. The edges of the mirrors should be touching closely. To avoid the separation and sliding of them, it is necessary to tape the touching place from the back of the mirrors and support them by several books at their back. Put a clock in front of the mirrors, first let it face one mirror, observe the number 3 and 9 on the clock face are in which side from you. Then let the centre vertical line is just face to the touching line of the mirrors, observe the image of the clock face again, compare the image with former. Repeat the experiment with a mark on your face.
28.2.14 Plane mirror
Use a single beam with the optical disc and a flat mirror element
28.2.15 Angle of incidence reflection
Aim a beam of light at a mirror at the centre of a disc. Rotate the disc.
28.2.16 Diffuse reflection
Hold frosted glass at various angles in a beam of light focussed on the wall.
28.2.17 Scattering with aluminium foil
Reflect light off a sheet of aluminium foil then crumple and flatten it to create many facets.
28.2.18 Reflection normal and grazing
Place a lantern and piece of clear glass midway between two walls and show the difference between reflecting by grazing on one wall and normal reflection on the other.
28.2.19 Corner cube, corner reflector
Three reflectors are placed on the inside corner of a box corner reflector. Two mirrors at 90 degrees or three mirrors mutually perpendicular. Look at your image in a corner cube.
28.2.20 Mirrors at an angle
A candle placed between angled mirrors forms multiple images. Two hinged front surface mirrors show multiple images of an object placed between them. Place a light between two mirrors hinged together and standing vertically. Place a sheet of clear glass between the mirrors forming an isosceles triangle.
28.2.21 Parallel mirrors
An infinite number of images are formed with a candle between parallel images.
28.2.22 Candle in a glass of water
Place a candle in front of a sheet of glass with a glass of water an equal distance behind the glass. Observe the image of the candle in the glass of water behind. Do the experiment with the entire apparatus on a rotating table.
28.2.23 Location of image
Place a sheet of glass between a burning candle and a glass of water so the image of the candle appears in the glass.
28.3.1 Spherical mirrors
Blackboard optics, curved mirrors, concave mirror, convex mirror
The distance to the centre of curvature is twice the distance to the principal focus. Spherical mirror formula: If u = object distance from mirror, v = image distance from mirror and f = focal length of mirror, then 1 / f = 1 / u + 1 / v. Magnification = height image / height object = v / u.
Concave mirrors (converging mirrors)
All rays parallel to the principal axis meet at the principal focus on the principal axis. A real image forms when the object is further than one focal length.
Convex mirrors (diverging mirrors)
All rays parallel to the principal axis through the mirror appear to come from the principal focus behind the mirror. The images that are always virtual, upright, diminished, and less than one focal length.
28.3.2 Concave and convex mirrors
Shine parallel beams at convex and concave mirrors. Use a thread screen for display. Mount either concave or convex mirrors in an optical.
28.3.4 Reflection from a concave mirror (converging mirror)
See diagram 28.3.4: Real image | See diagram 28.3.4.1: Virtual image | See also 2.0.5: Conic sections, parabola | See also 2.0.6: Parabola equation
For most spherical and parabolic mirrors, all rays parallel to the principal axis through the mirror either meet at a point on the principal axis called the principal focus, F, for converging or concave mirrors, or appear to come from such a point behind the mirror for diverging or convex mirrors. The centre of curvature, C, for a spherical mirror is twice the distance of the principal focus, F, from the mirror. Use the Cartesian co-ordinate sign convention: 1 / v + 1 / u =1 / f. Real images from a concave mirror forms when the object is further than one focal length (distance f) from the mirror. Where u is the object distance from the mirror, v is the image distance from the mirror, So is the object distance from the principal focus Si is the image distance from the principal focus, f is the focal length of the mirror, Ho is the height of the object, Hi is the height of the image. Virtual images occur when the object is less than one focal f length from the concave mirror.
1. Observe the reflection and convergence of a parallel sided beam, by using a large metallic ring with plating as a concave mirror.
2. Use a concave mirror. Draw a vertical line on the side of a cylinder made up of hard cardboard then draw another opposite line; bisect the cylinder along the two lines with a paper knife, paste the inside of one half to make it tidy. Insert a flash board with many slits into the ray box made at experiment 28.1.1 and use a cardboard to shade the light rays emitting from bottom so that a parallel sided beam is obtained. Observe the reflection and convergence of the parallel sided beam at the concave mirror and try to measure its focal point.
3. Bisect a cylinder and paste the outside of one half with silver paper to get a convex mirror. Also get a parallel sided beam and observe the reflection and divergence of the parallel sided beam at the convex mirror. Convex mirrors produce virtual, upright, diminished images, and inside F.
28.3.5 Reflection from a convex mirror (diverging mirror) convex surface
See diagram 28.3.5
Observe the reflection and divergence of a parallel sided beam, by using the side of a water bottle with plating or stainless steel kettle as a convex mirror.
28.3.6 Spherical aberration in a mirror
Shine parallel rays at spherical and parabolic mirrors noting the difference in aberration.
28.3.7 Variable curved mirrors
Aluminized Mylar stretched over a coffee tin makes a variable positive or negative mirror when the coffee tin is pressurized or evacuated.
28.3.8 Mirror and rose, flower in a vase
A hidden flower at the centre of curvature of a parabolic mirror appears in an empty vase.
28.3.9 Cold candle
Hold your finger in the inverted image of a candle burning at the centre of curvature of a parabolic mirror.
28.3.10 Amusement park mirrors
Cylindrical mirrors are made with 25 cm of curvature. View the image of your nose in a 1 cm diameter steel ball through a short focal length lens.
28.3.11 Energy at a focal point
1. Use a magnifier to focus sunlight on your arm!
2. Remove the projection head of an overhead projector and hold a piece of paper at the focal point until it bursts into flame.
28.4.01 Methods to find refractive index
Find the refractive index by the method of real and apparent depth, from air to glass, refraction by a prism.
Refraction in a lens, convex and concave lens, principal focus, lens.
Use optics kits to examine refraction and total internal reflection, the application of prisms to illustrate refraction, total internal reflection, and spectra, relative refractive indices, refraction in thin films and path difference, thin films, meniscus lenses
Snell's law: sin i / sin r = refractive index, n. Relative refractive index of glass is from air to glass or glass to air. Absolute refractive index glass is from vacuum to glass or glass to vacuum. Speed of light in a medium changes with Snell's law. When looking from air into a more refractive medium, e.g. water, objects appear to be at a shallower depth.
Apparent depth in water = real depth X refractive index air / refractive index water. 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.
Refraction at flat surfaces
Blackboard optics, red sunset, blue sky, rainbow, refractive index, refraction by a prism, definition of absolute refractive as sine ratio of the angles of incidence and refraction and velocities of light in the media, n1v1 = n2v2, quantitative treatment of critical angle and total internal reflection, optical fibre technology
Refraction is the change in direction of light as it crosses a boundary from one optical medium (such as glass) into another (such as air). Light bends towards the normal when entering a medium that is optically more dense, and away from the normal when entering an optically less dense medium. Light paths are reversible for refraction.
Laws of refraction
The incident ray, refracted ray, and normal to the boundary at the point of incidence, all lie in the same plane. Refractive index, n = sin i / sin r, where medium x is air and y is another medium (n >l). Absolute refractive index of any medium is the ratio sin i / sin r for light passing from a vacuum into that medium.
(a) 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.
(b) 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.
(c) 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. You can use prisms to change direction of light by total internal reflection. If glass has a critical angle of 42o, light entering a triangular right angle prism such that the angle of incidence to the glass / air interface is 45o will be totally internally reflected at an angle of 45o. The prism acts like a mirror.
Coherent light is light which is "in phase". A laser (Light Amplification by Stimulated Emission of Radiation) is a powerful source of coherent light. Two point sources of coherent light can be produced by directing any light through a single narrow slit then through a double slit arrangement
28.4.1 Refractive index of ice
Freeze water by pumping in a hollow acrylic prism and measure the minimum deviation.
28.4.2 Disappearing eye dropper
Place an eyedropper in a liquid with an index of refraction matched to the glass.
28.4.3 Refraction with shadow and cube
A shadow projected through a glass cube has a different length than normal.
28.4.4 Mesh on wall
Use a mesh projected on the wall and measure offset of a vertical wire.
28.4.5 Abbe refractometer
A liquid separates the hypotenuses of two right angle prisms.
28.4.6 Mirage
The image from a slide projector is directed just above a brass plate heated with a burner.
28.5.1 Refraction through glass block
A single beam of light on the optical disc is used to show refraction through a rectangular block of glass.
28.5.2 Refraction tank, ripple tank, aquarium
Rotate a beam of light in a tank of water containing some fluorescein.
28.5.3 Refraction model
An axle with independent wheels rolls down an incline with one wheel on cloth the other on the plain board.
28.5.4 Coin in a cup
Pour water into a beaker until a coin at the bottom previously hidden by the side is visible.
28.5.5 Light in a tank
Position a lamp in an opaque tank so that you cannot see the filament. Add water to the tank until you can see the light from the filament over the edge of the tank.
28.5.6 Stick in water, bent stick
A stick appears bent when inserted into water at an angle.
28.5.7 Acrylic / lead glass refraction
Hold a stick behind stacked lead glass and acrylic blocks. The image of the stick is shifted when viewed off the normal to the surface of the blocks.
28.5.8 Minimum angle of deviation, minimum deviation of a prism
At minimum deviation light reflected off the base is parallel to that passing through an equilateral prism.
28.5.9 Refraction of light, air to water
See diagram 28.3.6
Observe the reflection of a beam of light from air into water by adding drops of milk to water in a glass and stir it until the colour is uniform. Put the glass of milky water in the sunlight. Make a small hole in a piece of cardboard. Hold the piece of cardboard so that a beam of sunlight hits the side of the glass below the level of the milky water. Note the direction of the beam through the water. Raise the piece of cardboard so that the beam of sunlight strikes the surface of the milky water. Observe how the beam changes direction where it hits the water - the beam is refracted. Note that the angle between the surface of the milky water and the refracted beam depends on the angle between the water and in incoming, incident, beam. To observe clearer, place another cardboard above the cup to shade the cup.
28.6.0 Total internal reflection
See diagram 4.127.3
1. Drill a small hole in the side near the bottom of a tall drink-can and plug the hole. Fill the drink-can with water and place it on the edge of a table over a basin. Darken the room. Shine an electric torch down into the drink-can. Remove the plug to let the water stream fall into the basin. The light from the torch bends with the falling stream to form a light spot on the bottom of the basin because of the total internal reflection of light on the interface between water and air. Some rays are refracted to your eyes. This is the principle of fibre optics cable.
2. Put an electric torch in the spout of a watering can.
3. To make an attractive table lamp by put you light source facing upwards in a light proof container like a flower vase. Then place thin bending plastic tubes in the flower vase.
28.6.1 Optical disc with prism semicircle
A single beam of light on the optical disc shows total internal reflection when passed through a prism. A beam of light entering a semicircular glass normal to the curved surface is reflected off the flat side.
28.6.2 Critical angle in ripple tank, refraction tank, aquarium
A beam in a tank of water is rotated until there is total internal reflection at the surface. Adjust the path of a beam with mirrors in a tank of water with fluorescein to show total internal reflection.
28.6.3 Critical angle and total internal reflection
1. Shine a beam through the side of a tank containing fluorescein. Rotate a mirror in the tank so the beam passes through the critical angle. Vary the angle of incidence of ripple tank waves to a boundary with water depths of 13 and 3 mm.
28.6.5 Light below surface
An underwater light illuminates powder on the surface of water to form a central spot of light.
28.6.6 Water / benzol surface
Total internal reflection from a water / benzol surface.
28.6.7 Black ball turns silver
A soot covered ball appears silver under water due to reflected light from air trapped on the surface of the ball. forming an air water interface.
28.6.8 Diamond
A thin beam of light is directed on a diamond and the reflections are projected onto a cardboard.
28.6.9 Right angle prism inverter
A right angle prism placed in a projected beam inverts the image. A beam entering the hypotenuse of a right angle prism is inverted and reversed.
28.8.0 Thin Lens
Blackboard optics, convex and concave thin lens, light rays through lenses, optical benches to examine the properties of thin lenses and mirrors, location of virtual images by parallax
Lens formula: 1 / u + 1 / v = 1 / f
Magnification = height image / height object = v / u.
Concave lens (diverging lens)
Parallel light rays diverge as if coming from the principal focus. Images are always virtual, upright, diminished, and less than one focal length from the lens.
The image formed by a diverging lens is virtual, erect, and diminished, and always lies on the same side of the lens as the object does. The virtual image of an object is always closer to the lens than the object itself. The image formed by a diverging lens is virtual, erect, and diminished, and always lies on the same side of the lens as the object does. The virtual image of an object is always closer to the lens than the object itself.
Convex lens (converging lens)
Parallel light rays converge through the principal focus. Real image forms when object is more than one focal length from the lens. Virtual image forms when object is less than one focal length from the lens. Convex (converging) lenses are wider in the middle than at the edges. Parallel light converges through a point called the principal focus, F.
Images in a convex (converging) lens: Real images form when an object is further than one focal length from the lens. 1 / v - 1 / u = 1 / f, where u is the object distance from the lens, v is the image distance from the lens, f is the focal length of the lens. Magnification = Hi / Ho = f / So = Si / f = v / u, where Ho is the height of the object, Hi is the height of the image, So = object distance from the principal focus, Si = image distance from the principal focus. Virtual images form when the object is less than one focal length from the lens.
The types and positions of the image formed by a converging lens depend on u, v, f, and their relationship. Image is a picture or appearance of a real object, formed by light that passes through a lens or is reflected from a mirror. If rays of light actually pass through an image, it is called a real image. A mirror forms an image by the law of reflection. The focal length of a mirror depends only on geometrical considerations because the properties of the material do not affect the focal length when light reflects from a mirror surface. For the lens, the image forming properties depends on refraction through the lens material thus the focal length will depend both on geometric factors and the index of refraction of material of the lens. For both lenses and mirrors, the image and object distances are related by the same equation: u-1+ v-1 = f-1 (1 / f = 1 / u + 1 / v), where u is the distance from the object to the optical centre of the lens or to the mirror pole viz. object distance, v is the distance from the image to the optical centre of the lens or to the mirror pole viz. image distance, f is the focal length of the lens, which is positive for converging lenses and negative for diverging lenses.
The types and positions of the image formed by a converging lens depend on u, v, f, and their relationship. See following table of the image formed by a converging lens and applications:
Position
Number		 Position of object Position of image Description of image Application
1 u = infinity v = f Image on other side of lens Find focal length
2 infinity >u >2f f < v < 2f Real, inverted, diminished Eye, camera
3 u = 2f v = 2f Real, inverted, same size -
4 2f >u >f 2f < v < infinity Real, inverted, magnified Slide projector
microscope
5 u = f v = infinity No image Searchlight
6 f >u >0 v < 0 Virtual, upright, magnified, image on same side of lens Magnifying glass
28.8.1 Convex lens forms an image
See diagram 4.128
Lens formula and magnification, characteristics of images formed by thin lenses including a lens equation relating object distance, u, image distance, v,  and focal length, f,  and suitable conventions
1 / v + 1 / u = 1 / f, magnification, M = Hi / H0, ray diagrams to show image formation with thin lenses, combinations of lenses
Making the scene "shine" on a piece of paper Use a piece of paper to receive the real image formed by a convex lens. Close the door of a room and cover its window just leave a light beam at the corner. Hold a convex lens facing the scene outside window at the corner. Move a piece of white paper parallel to the lens to close the lens slowly. Observe the image on the paper and compare it with the practical scene.
28.8.3 Concave lens, focal length of concave lens using lens formula
See diagram 28.4.9
Concave (diverging) lenses are narrower in the middle than at the edges. Parallel light diverges as if coming from a point called the principal focus, F.
Insert the pin into the versatile stand to fix the pin. Place the needle shaped object O in front of the concave lens. The pin as a searcher S searches the position at which S coincides with the object's image I between O and lens L, here you may see both I and S through L's upper. Adjust the position of S to decrease the optical parallax between S's visible part and I. Measure the object distance u and the image distance v. Repeat the experiment with different u 4 times. Calculate the focal length of the concave lens with following formula: 1 / v + 1 / u = 1 / f.
28.8.4 Ripple tank convex lens, concave lens
Refraction due to depth differences over a lens shaped area in the ripple tank.
28.8.5 Ray tracing with lenses
Examine parallel rays passing through a lens element and converging.
28.8.6 Thin lens projection
Project the filament of a lamp with a thin lens on the wall.
28.8.7 Real image formation
With a source and screen at the ends of a long optical bench show the two positions a lens will produce an image.
28.8.8 Projected arrow with lens
Use an illuminated arrow with a converging lens to project an image on a screen.
28.8.9 Thin concave lens
Try to project an image with a thin concave lens.
28.8.10 Effect of medium on focal length
Find the focal length of a lens then find the focal length of the same lens in water.
28.8.11 Pinholes projected with lens
Pinholes are pricked in a black paper covering a long filament bulb. Bring the multiple images into one image with a converging lens. Connect a microwave lens and prisms of stacks of properly contoured aluminium sheets separated by just over one half the wavelength microwave lens.
28.9.0 Pinhole camera
The pinhole camera is just a light-proof box with a pinhole about 0.5 mm in the centre of one side instead of a lens. The opposite side of the box can be a translucent screen or photographic film that can be exposed. Some modern photographers use the pinhole camera to obtain its unique soft images and distortions in perspective - images that the human eye would never see. The pinhole camera is similar to the "camera obscura".
28.9.3 Fish-eye camera
A pinhole camera filled with water or solid Lucite gives a fish-eye view
28.10.0 Thick Lens
Plastic lenses, Fresnel lens
28.10.1 Depth of focus
Use a 12 cm long glowing wire as an extended object for showing the effect of stopping down a lens.
28.10.2 Chromatic aberration
Fringes of colour about an image is caused by a lens with different refractive index for different wavelengths that focus at different distances from the lens and with different magnification. The problem occurs in colour photography and is solved with special lenses or special combinations of lenses. A diaphragm moved near the focus selects red or blue light from beams passing through the edge of a lens. Project spots of light on a screen from several points on a lens.
28.10.3 Barrel and pincushion distortion
Project an illuminated wire mesh with a large lens. Place a diaphragm between the lens and the mesh for barrel distortion and between the lens and the screen for pincushion distortion.
28.10.4 Off axis distortion
Parallel rays of light pass through a lens element held off axis.
28.10.5 Astigmatism
Focus light from a circular hole on a screen then add a cylindrical lens. An illuminated wire mesh is projected onto a screen with a short focal length condenser lens Turn the lens about an axis parallel to either set of wires and the horizontal and vertical wires will focus at different points.
28.10.6 Water lens
A beam of light is directed through a round flask filled with water.
28.10.7 Fillable air lenses
Convex and concave lenses are filled with water and air.
28.10.8 Spherical lens
Compare a thermometer at the centre of a water filled flask to one at the far side.
28.10.9 Wine bottle lens
Fill a round flask with a wine bottle bottom (arch-shaped bottom) inverted with water and fluorescein to show diverging light.
28.10.10 Watch glass lens
A vertical lens can be formed by pouring various liquids into a watch glass.
28.10.11 Optical instruments, optical equipment, smoke box, ray box, water lens, spectroscope, magnifying glass, compound microscope, reflecting telescope, Young's experiment
28.11.1 Simple magnifier
See diagram 4.130
Make a single turn of copper wire around a nail to form a loop. Dip the loop into water, take it out and look through it. Such a lens may magnify four or five times. Tap the wire sharply against the edge of the glass so that a drop of water falls off. Because of adhesion between the wire and the water, the liquid remaining will form a lens, which is very thin at the centre, i.e. a concave lens.
28.11.2 Water drop magnifier
Place a drop of water carefully on a plate of glass. Bring your eye close to the drop and look at something small through the water drop and glass. The water drop serves as a simple magnifier.
28.11.3 Model refracting telescope
Arrange a long focus lens on the end of an optical bench  pointing at an object through the window. Bring a piece of white cardboard up on the opposite side of the lens to the place where the sharpest image of the scene is formed. Bring a short focus lens up behind the cardboard until the cardboard is a little nearer the lens than its focal length. Remove the cardboard and look through the two lenses at the object.
28.11.4 Projector for filmstrips or slides
See diagram 28.11.4
The base of the instrument is a piece of plywood 40 X 10 X 3 cm. A plywood board 10 cm wide and 25 cm long fits into a groove cut across the base. It serves as filmstrip carrier. A hole 35 by 23 mm cut in this wood serves as an “aperture” or gate to limit the light passing to one frame of the strip. Fix the strip close to the gate in a vertical position with staples made from wire paper clips. Bent them  to the width of the film and cut the ends short and sharpen them with a file. Then press them into position on the plywood board. No reels are necessary. The strip can be moved on from one frame to the next by pulling on the end of the film until there is sufficient 'curl' to hold it stationary.  The lamp is an automobile head lamp in a holder mounted on a block. It is adjustable so that it can be slid between two strips of wood nailed to the base. Use a carafe or flask of water as a condensing lens placed so that the whole of the gate is illuminated by the image of the lamp. When so positioned, the lamp and condensing flask are fixed in place with glue. The object lens is mounted on a piece of wooden doweling that is a tight fit in a hole drilled into a block of wood arranged, like the lamp support, to slide between two wooden guides. Adjust the lens by sliding the rod in or out of the hole so that the centre of the lamp, condenser and objective are all the same height above the baseboard.  Use a plywood,  metal or cardboard case to enclose the lamp and the condenser. Use the apparatus in a darkened room.
28.11.5 Microprojector
The optical system of this instrument is the same as that of the strip projector except that for microscope slides  use a very short focus objective to obtain high magnification. The lamp is a car headlight bulb. The condenser is a small glass bulb 1.5 to 2 cm in diameter. The object lens is the objective of a commercial microscope.  The base of the apparatus is a small wooden trough 10 X 7 X 4 cm,  made by nailing two strips of wood 4 cm wide to the sides of a piece measuring 10 cm X 5 cm X 1 cm.  An end plate to support the objective is a piece of plywood 9 cm X 7 cm with a 2.5 cm hole in it. Fix the end plate to the end of the trough.  Fit a rectangular lamp house into the channel. The lamp house has a car bulb and holder fixed inside a rectangular container. Drill holes drilled around the top and at the bottom to provide ventilation. A hole 1.5 cm in diameter serves to support the condenser. Use copper wire passing round the stem of the bulb and through holes punched through the tin to hold the condenser  in position. The slide holding the object to be projected fits into grooves cut across the edges of the channel, and is thus held in a vertical plane so that the light from the condenser passes through it. The microscope objective fits tightly into a hole in a piece of plywood, 7 X 4 cm, which is held in contact with the end plate by a  clip and  adjusted so that the lens lies on the axis of the optical system. To adjust the apparatus, move the slide, lamp house and condenser forward together until the light passes through the objective and forms an image  of a specimen 60 cm away from the end of the trough. When the correct position for the slide is found, make  saw cuts in the edge of the trough. This apparatus can also be used for projecting Newton's rings and diffraction phenomena.
28.11.6 Use a microscope as a microprojector
If a very bright light source is used, the image from the eyepiece of a compound microscope can be reflected on to a screen with a mirror. A  powerful slide projector is a good source of light.
4.142.1 Measure solar ultraviolet radiation
See also 3.50: Ozone, O3 | See also 36.0.17: Albedo
After Alflio Parisi and Michael Kimlin, Australian Science Teachers' Journal, 44 (3)
The risk of developing non-melanoma skin cancer is related to the cumulative ultraviolet radiation (UV) exposure. The risk of melanoma increases with the number of sunburns, specially during childhood. The UV waveband consists of UVA (320 to 400 nm), UVB (280 to 320 nm) and UVC (200 to 280 nm) wavelengths. (Note: nm = nanometre = 10 Angstrom units = 10-9 m.) No UVC reaches the Earth's surface because of absorption by oxygen and ozone in the atmosphere. The total solar UV radiation at the Earth's surface consists of a direct component and a diffuse component. The direct component comes in a direct path from the sun. The diffuse component is the radiation scattered by the atmosphere, clouds and the surroundings. The scattering is more significant at the shorter UV wavelengths. The reflected UV radiation is the UV reflected from any surface, e.g. the ground surface. The shorter wavelengths are the most damaging and produce the greatest erythema, redness of the skin due to dilation of the capillaries (sunburn), i.e. the UVB wavelengths. Take two sets of readings per day, at 10.30 am and 1.00 pm over a period of two weeks. Measure the total solar UV irradiance (UVTotal) with the meter pointing upwards. Measure the diffuse UV reflectance with the detector facing two ground surfaces, e.g. dead grass and asphalt. Cover the detector so that it is in shadow. Calculate the percentage reflectance (albedo) of the surface (R%), e.g. 3.3% for dead grass and 3.8% for asphalt: R% = (UVReflected / UVTotal) X 100. Albedo is the reflecting power of a non-luminous body. Plot the total and diffuse reflectance for two readings each day on a bar graph. Note the cloud cover at each measuring time. The total and diffuse UV radiation varies with the cloud cover. On the overcast days the diffuse irradiance forms a high relative proportion of the total UV irradiance. The relative proportions of the diffuse and total UV irradiance also vary with the seasons due to the change in solar zenith angle resulting in a different atmospheric optical path length. So there is a change in the amount of scattering and absorption in the atmosphere. A UV meter can be designed to have a response that approximates the response of human skin to UV radiation measures the erythemal UV irradiance or the UV irradiance weighted with the response of human skin.