2.2 Total internal reflection Disappearing pencil Criteria for total internal reflection Critical angle and refractive index Check-point 5 Examples of total internal reflection Check-point 6 1 2 3 Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Disappearing pencil Insert a pencil into an empty test tube. Put the test tube in a container filled with water, the pencil disappears! But it reappears if you add water into the test tube! Video 2.5 Disappearing pencil Book 3A Section 2.2 Total internal reflection

2.2 Total internal reflection Simulation 2.4 Total internal reflection Expt 2b Total internal reflection Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Experiment 2b Total internal reflection Direct a ray of light to enter the semicircular glass block from its curved edge towards its centre O. Slowly  the angle of incidence g and watch how the refracted ray changes. Video 2.6 Expt 2b - Total internal reflection Book 3A Section 2.2 Total internal reflection

1 Criteria for total internal reflection Three rays hitting the inside face of a semicircular glass block at different angles: The incident ray splits into two rays: a reflected ray inside the glass and a refracted ray in the air. Book 3A Section 2.2 Total internal reflection

1 Criteria for total internal reflection The incident ray also splits into two rays. Angle of refraction = 90° The refracted ray just manages to leave the glass surface. Book 3A Section 2.2 Total internal reflection

1 Criteria for total internal reflection The incident ray is totally reflected inside the glass. There is no refracted ray. Book 3A Section 2.2 Total internal reflection

1 Criteria for total internal reflection Critical angle (C ) : angle of incidence at which the r = 90° If i > C , the light ray will be totally reflected inside the glass block.  the surface acts like a mirror.  total internal reflection Book 3A Section 2.2 Total internal reflection

1 Criteria for total internal reflection Note: Total internal reflection only occurs for an incident ray in an optically denser medium. It does not occur when light passes from an optically less dense medium to an optically denser medium, no matter how large i is. Video 2.7 Total internal reflection in water Book 3A Section 2.2 Total internal reflection

2 Critical angle and refractive index Angle of incidence in a medium = C when angle of refraction in air = 90°, i.e. n sin C = 1  sin 90° n = 1 sin C or C = sin–1 n  n: refractive index of the medium Book 3A Section 2.2 Total internal reflection

2 Critical angle and refractive index The following figure shows how the reflected and refracted rays change: Example 7 Finding the path of a light ray Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 7 Finding the path of a light ray A light ray travelling in the direction EO in air enters a rectangular glass block. Angle of incidence = 30 Angle of refraction = 18 (a) Find the refractive index n of the glass block. sin a sin g n = = sin 30 sin 18 By Snell’s law, = 1.62 Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 7 Finding the path of a light ray (b) Find the critical angle C for the glass-air interface. C = sin–1 1 n = sin–1 1 1.62 = 38.1 Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 7 Finding the path of a light ray (c) If the ray is incident on surface BC , from which surface and at what angle will it leave the block? The ray comes out from surface AD. The emergent angle from the normal is 60°. Book 3A Section 2.2 Total internal reflection

2 Critical angle and refractive index Video 2.8 Disappearing button Video 2.9 ‘Magic Cube’ Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Check-point 5 – Q1 Which of the following angles indicates the critical angle for a glass-air interface? B A C D Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Check-point 5 – Q2 Complete the following table. Medium Refractive index Critical angle Water 1.33 Perspex 1.50 Glass 1.50 – 1.70 Crystal 30.0 Diamond 24.4 48.8 41.8 36.0 – 41.8 2.00 2.42 Book 3A Section 2.2 Total internal reflection

3 Examples of total internal reflection a Optical fibres A light ray can pass along a glass fibre from one end to the other. The fibre ‘guides’ light by a series of total internal reflections. Light bounces along the inner walls. Video 2.10 Simple optical fibre Video 2.11 Water light guide Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection a Optical fibres Optical fibres made of very pure glass very thin and flexible used in telecommunications (flashes of light from a laser send signals at high speed) used as ‘light guides’ for doctors to see inside the human body Video 2.12 Endoscope Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection a Optical fibres Example 8 Optical fibres Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 8 Optical fibres A simple optical fibre is made of a plastic core with no outer cladding. Refractive index of the plastic = 1.6 A ray of light is incident from air on one end of the fibre at an angle of 60°. Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 8 Optical fibres (a) Calculate  and  . By Snell’s law, sin a sin g ng = sin 60 sin  = 1.6  = 32.8  = 90 –  = 90 – 32.8 = 57.2 Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 8 Optical fibres (b) Calculate the critical angle for the core-air interface. Is the ray totally reflected inside the core? Critical angle of the plastic core 1 n = sin–1 = sin–1 1 1.6 = 38.7   > C  the ray is totally reflected inside the core. Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 8 Optical fibres (c) If the core is coated with a cladding (n = 1.1), critical angle of the core-cladding interface = ? By Snell’s law, n1 sin 1 = n2 sin 2 1.6  sin C = 1.1  sin 90° C = sin–1 1.1 1.6 = 43.4 Book 3A Section 2.2 Total internal reflection

3 Examples of total internal reflection b Using prisms as mirrors A plane mirror consists of: a glass sheet coating a reflective material (silvering) on the back surface Multiple reflections between the front and the back surfaces form fainter images (I1, I3, …)  making the main image I2 less clear. Book 3A Section 2.2 Total internal reflection

b Using prisms as mirrors A prism works like a mirror if light rays are incident on its inside face at an angle > C. Prisms do not form multiple images used in many optical instruments for quality images e.g. cameras, periscopes and binoculars. Book 3A Section 2.2 Total internal reflection

b Using prisms as mirrors Prisms can also be found in headlight reflectors in cars and cat’s eyes on the road. Simulation 2.5 Light maze Book 3A Section 2.2 Total internal reflection

3 Examples of total internal reflection c Mirages On a hot day, sometimes the road at a distance ahead appears wet and reflective  the reflection of the sky  mirage (commonly occurs in deserts) Video 2.13 Mirage in a water tank Video 2.14 Mirage at the airport Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection c Mirages Air near the ground: hotter, lower refractive index  light from the sky is gradually refracted more towards the horizontal. total internal reflection finally occurs see the image of the sky when looks down light from the sky cool air total internal reflection occurs here warm air hot air image of the sky Book 3A Section 2.2 Total internal reflection

3 Examples of total internal reflection d Diamonds large refractive index  easily reflect light which goes into them  sparkle facets have to be cut at carefully chosen angles, or light may escape through the bottom or sides Example 9 Superior mirage Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 9 Superior mirage In a special case of mirage, commonly known as a superior mirage, an observer may see an inverted island that floats in the sky. Such a mirage appears when the temperature of the air increases with height. This is most likely to form when the sea is much colder than the atmosphere. The air near the sea surface has a higher refractive index. Light travelling upwards is gradually refracted, but in the opposite way from an ordinary mirage. This is why we see the illusion in the sky instead of on the ground. Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 9 (a) How does the refractive index of air vary with height when a superior mirage is formed? Refractive index of air decreases as height increases. Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 9 Superior mirage (b) Explain how the inverted image of the island can be formed in this way. Refractive index of air   light from the island is gradually refracted more and more towards the horizontal meets air at an angle > C  total internal reflection occurs  the light then travels downwards  see the image of the island in mid-air Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 9 Superior mirage (c) Sketch a ray diagram to show how the superior mirage is formed. Mark the positions of the object and the image. Book 3A Section 2.2 Total internal reflection

3 Examples of total internal reflection Diamond and glass jewellery Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 10 Diamond and glass jewellery Refractive index of diamond = 2.42 Refractive index of glass = 1.50 (a) Find the critical angles for a diamond-air interface and a glass-air interface. = sin–1 1 2.42 For diamond, C = 24.4 = sin–1 1 1.50 For glass, C = 41.8 Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 10 Diamond and glass jewellery (b) Can glass jewellery be cut to give similar brilliance to that of a diamond? Why? C for a glass-air interface is much larger much smaller amount of light going into glass jewellery is totally internally reflected does not have the same brilliance as diamond jewellery Book 3A Section 2.2 Total internal reflection

3 Examples of total internal reflection e Fish-eye view A fish or a diver underwater can see everything above the water surface, but the view is squeezed into a cone with an angle ~ 98°. Outside the cone, water surface looks like a mirror. Video 2.15 Total internal reflection in a fish tank Example 11 Diameter of the diver’s view Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 11 Diameter of the diver’s view A diver (eyes 0.5 m below surface) looks upwards. Refractive index of water = 1.33 (a) Angle of the fish-eye view he sees = ? 1 n = sin–1 C = sin–1 1 1.33 = 48.8 Angle of the fish-eye view = 2 = 2C = 2  48.8 = 97.6 Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Example 11 Diameter of the diver’s view (b) Diameter of the diver’s view = ? Diameter of the diver’s view = 2  radius of the cone = 2  0.5  tan  = 2  0.5  tan 48.8 = 1.14 m Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Check-point 6 – Q1 Some optical fibres are attached to a torch. What happens to the fibres when the torch is switched on? A B Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection Check-point 6 – Q2 A horizontal light ray is incident on a prism. Which ray diagram is correct? (Critical angle of the prism = 42°) A B C Book 3A Section 2.2 Total internal reflection

Book 3A Section 2.2 Total internal reflection The End Book 3A Section 2.2 Total internal reflection