Refraction through a glass slab, laws of refraction and refractive index
Light bends when it passes obliquely from one medium to another because its speed changes. Through a glass slab, the emergent ray is parallel to the incident ray.
What refraction is
Refraction is the change in direction of light when it passes obliquely (at a slant) from one transparent medium into another. It happens because light travels at different speeds in different media. A rarer medium is one in which light is faster, such as air. A denser medium is one in which light is slower, such as glass or water. Going from rarer to denser, the ray bends towards the normal. Going from denser to rarer, it bends away from the normal. A ray that falls along the normal (at 90° to the surface) goes straight through without bending. You see refraction every day. A pencil in a glass of water looks bent. A pond looks shallower than it is. A lemon in a glass of water looks bigger.
Activity and how to draw: path of a ray through a rectangular glass slab
You need a drawing board, a white sheet, a rectangular glass slab, four pins, a protractor and a scale.
- 1Fix the white sheet on the board. Place the slab in the middle and draw its outline ABCD with a sharp pencil. AB is the face the light will enter.
- 2Draw a straight line slanting towards face AB, meeting it at point O. Fix two pins, P and Q, upright on this line, a few cm apart.
- 3Look at P and Q through the opposite face CD. Fix two more pins, R and S, so that they appear in one straight line with the images of P and Q.
- 4Remove the slab and the pins. Join the marks of R and S and extend the line to meet CD at O′. Join O and O′.
- 5Draw normals (dotted lines at 90° to the faces) at O and O′. Label the incident ray PQO, the refracted ray OO′ and the emergent ray O′RS.
- 6Measure ∠i at O, between the incident ray and the normal. Measure ∠r, between OO′ and the same normal. Measure ∠e at O′, between the emergent ray and the normal there. Extend the incident ray beyond O as a dotted line to show the lateral displacement (the sideways gap between it and the emergent ray).
- 7Observe: ∠r is smaller than ∠i, so the ray bent towards the normal inside the glass. ∠e = ∠i, so the emergent ray is parallel to the incident ray but shifted sideways.The bending at the two parallel faces is equal and opposite.
Laws of refraction and refractive index
- Law 1: the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
- Law 2 (Snell's law): for a given pair of media and a given colour of light, sin i / sin r = constant. Here i is the angle of incidence and r is the angle of refraction.
- This constant is the refractive index of the second medium with respect to the first, written n₂₁.
- Refractive index also compares speeds: n₂₁ = (speed of light in medium 1) ÷ (speed of light in medium 2) = v₁/v₂.
- The absolute refractive index of a medium compares it with vacuum: n = c/v, where c = 3 × 10⁸ m/s is the speed of light in vacuum and v is its speed in the medium.
- A medium with a higher refractive index is optically denser: light is slower in it. Optical density is not mass density. Kerosene (1.44) is optically denser than water (1.33), yet it floats on water.
- Refractive index is a ratio of two speeds, so it has no unit.
Absolute refractive index of some media
| Medium | Refractive index |
|---|---|
| Air | 1.0003 |
| Ice | 1.31 |
| Water | 1.33 |
| Kerosene | 1.44 |
| Crown glass | 1.52 |
| Rock salt | 1.54 |
| Ruby | 1.71 |
| Diamond | 2.42 (the highest in this list, so light is slowest in diamond) |
Finding refractive index from the speed of light
Light travels at 2.25 × 10⁸ m/s in water. (a) Find the refractive index of water. (b) The refractive index of crown glass is 1.52. Find the refractive index of crown glass with respect to water.
- Given: c = 3 × 10⁸ m/s, speed in water v = 2.25 × 10⁸ m/s.
- (a) Formula: n = c/v.
- n(water) = (3 × 10⁸ m/s) ÷ (2.25 × 10⁸ m/s) = 3 ÷ 2.25 = 1.33 (rounded to two decimal places).
- (b) Formula: n(glass with respect to water) = n(glass) ÷ n(water).
- = 1.52 ÷ 1.33 = 1.14 (rounded to two decimal places).
(a) The refractive index of water is about 1.33 (no unit). (b) Crown glass with respect to water is about 1.14, so light bends towards the normal when it goes from water into this glass.
A coin in a tumbler of water, or a fish in a temple tank, looks closer to the surface than it really is. Light bends away from the normal as it leaves the water, so a pond can be deeper, and more dangerous, than it looks.
1 marks: “Diamond has a refractive index of 2.42. Compare the speed of light in diamond with its speed in vacuum.” Light in diamond moves at 1/2.42 of its speed in vacuum: v = c/n = (3 × 10⁸) ÷ 2.42 ≈ 1.24 × 10⁸ m/s.
3 marks: “State the two laws of refraction. Find the speed of light in rock salt, whose refractive index is 1.54 (c = 3 × 10⁸ m/s).” Same plane; sin i / sin r = constant. v = c/n = (3 × 10⁸) ÷ 1.54 ≈ 1.95 × 10⁸ m/s.
5 marks: “Draw a labelled diagram of the refraction of light through a rectangular glass slab. Mark ∠i, ∠r, ∠e and the lateral displacement. Why is the emergent ray parallel to the incident ray?” Slab with normals at both faces; ∠r smaller than ∠i at entry; ∠e = ∠i; the bending at the two parallel faces is equal and opposite, so the ray comes out parallel, only shifted sideways.
Fast to Slow bends Towards (FST): air to glass, the ray leans towards the normal. Slow to fast, it leans away. A slab bends the ray in and out by the same amount, so it comes out parallel.