A straw looks bent in a glass of water, and a swimming pool looks shallower than it is. Light changes direction when its speed changes.
Refraction is the bending of light when it passes from one medium to another, because its speed changes. The incident ray, the refracted ray and the normal lie in one plane. Snell's law states that sin i ÷ sin r is constant for a given pair of media. This constant is the refractive index, n = sin i ÷ sin r = speed of light in vacuum ÷ speed of light in the medium. Light entering a denser medium bends towards the normal.
The refractive index of glass is 1.5. Find the speed of light in glass. (c = 3 × 10⁸ m/s)
v = c ÷ n = 3 × 10⁸ ÷ 1.5 = 2 × 10⁸ m/s
The refractive index of water is 4/3. Find the speed of light in water.
3 × 10⁸ ÷ (4/3) = 2.25 × 10⁸ m/s
A ray in air strikes glass (n = 1.5) at i = 45°. Find the angle of refraction.
sin r = sin 45° ÷ 1.5 = 0.707 ÷ 1.5 = 0.471, so r ≈ 28°; the ray bends towards the normal
Seen from above, an object under water appears raised, because the rays bend away from the normal as they leave the water. The refractive index is n = real depth ÷ apparent depth, so the apparent depth is always less than the real depth.
A tank of water (n = 4/3) is 12 cm deep. What is its apparent depth?
Apparent depth = real depth ÷ n = 12 ÷ (4/3) = 9 cm
Why does a pool look shallower than it really is?
Rays from the bottom bend away from the normal as they leave the water, so they appear to come from a point nearer the surface
The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°, and sin c = 1 ÷ n. Total internal reflection occurs when light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle. It is used in optical fibres, in prisms in binoculars and in the sparkle of diamonds.
Find the critical angle for glass of refractive index 1.5.
sin c = 1 ÷ 1.5 = 0.667, so c ≈ 41.8°
State the two conditions for total internal reflection.
The light must travel from a denser to a rarer medium, and the angle of incidence must be greater than the critical angle
1. What is meant by refraction of light?
2. State Snell's law.
3. Write the relation between refractive index and the speed of light.
4. Find the speed of light in glass of refractive index 1.5. (c = 3 × 10⁸ m/s)
5. Does a ray entering glass from air bend towards or away from the normal?
6. A tank of water (n = 4/3) is 12 cm deep. What is its apparent depth?
7. Define the critical angle.
8. State the conditions for total internal reflection.
9. Find the critical angle of glass of refractive index 1.5.
10. Name one use of total internal reflection.