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Refraction

Waves, sound and light · level 5, lesson 5 of 6

A question to start

A straw standing in a glass of water looks bent at the surface. The straw is straight. What is bending?

The idea

Light is slower in water and glass than in air. When light crosses from one into the other at an angle, it changes direction. This is refraction.

  • Going into a slower medium (air → glass), light bends towards the normal.
  • Going into a faster medium (glass → air), it bends away from the normal.
  • Hitting the surface straight on, along the normal, it slows down but does not bend.

How much a material slows light is given by its refractive index:

\[n = \frac{c}{v}.\]
Material \(n\) Speed of light in it
Air about 1.000 \(3.00\times10^8\) m/s
Water 1.33 \(2.26\times10^8\) m/s
Glass about 1.5 \(2.0\times10^8\) m/s
airglass: slowerbends towardsthe normalnormal

The frequency does not change as the light crosses; the speed and the wavelength both drop.

Worked examples

1. Speed in water. \(v = c/n = 3.00\times10^8/1.33 = 2.26\times10^8\) m/s.

2. The straw. Light from the part of the straw under water bends as it leaves the water, so it seems to come from higher up. The straw looks bent at the surface.

3. Wavelength in glass. Green light of 550 nm in air has, in glass with \(n = 1.5\), a wavelength of \(550/1.5 = 367\) nm.

Try it

  1. What is refraction?
  2. A ray passes from water into air at an angle. Does it bend towards or away from the normal?
  3. Light travels at \(1.24\times10^8\) m/s in diamond. Find diamond's refractive index.
  4. Why does a ray that hits glass straight on, along the normal, not bend?
Answers
  1. The change of direction of a wave as it crosses into a medium where its speed is different.
  2. Away from the normal.
  3. \(n = 3.00\times10^8/1.24\times10^8 = 2.42\).
  4. Every part of the wavefront slows down at the same moment, so it changes speed without turning.

Common mistake

"Refraction changes the frequency." The frequency stays the same. Only the speed, the wavelength and (at an angle) the direction change.

Where it leads