3.4 - Refraction

What refraction is

• Refraction is when a wave changes direction as it crosses a boundary between two materials at an angle.
• The normal is an imaginary line drawn at right angles to the boundary, at the point where the wave meets it.
• A wave bends only if it hits the boundary at an angle to the normal.
• A wave travelling along the normal carries on in the same direction without bending, although its speed and wavelength still change.

Which way the wave bends

• A wave that slows down as it crosses a boundary bends towards the normal.
• A wave that speeds up as it crosses a boundary bends away from the normal.

For example, light passing from air into glass slows down and bends towards the normal. Passing back out into air, it speeds up and bends away from the normal.

Why waves refract - The change in speed

• A wave refracts because it changes speed when crossing into a different material.
• If the wave meets the boundary at an angle, this change in speed makes it change direction.
• The bigger the change in speed, the more the wave bends.

Wavefront explanation

1. When a line of wavefronts hits a boundary at an angle and slows down, the end that crosses first slows down before the other end.
2. That end travels a shorter distance in the same time, so the wavefront swings round and changes direction.
3. The wavefronts also get closer together, showing that wavelength has decreased.

Frequency stays the same, so wavelength changes

When a wave crosses a boundary, its frequency does not change. From the wave equation ($v=f\lambda$), if speed $v$ changes while frequency $f$ is constant, the wavelength $\lambda$ must change:

• If the wave slows down, its wavelength decreases.
• If the wave speeds up, its wavelength increases.

Optical density

• Optical density is a measure of how quickly light travels through a material - the higher the optical density, the slower light travels.
• Light slows down and bends towards the normal when entering a more optically dense material.

Drawing a ray diagram for refraction

How to draw it

1. Draw the boundary between the two materials.
2. Draw the normal as a dotted line at right angles to the boundary.
3. Draw the incident ray meeting the boundary at the normal. The angle of incidence ($i$) is between the incident ray and the normal.
4. Draw the refracted ray continuing into the second material with an arrow showing its direction. The angle of refraction ($r$) is between the refracted ray and the normal.

Comparing the angles

• Into a more optically dense material - The ray slows down and bends towards the normal, so the angle of refraction is smaller than the angle of incidence ($r<i$).
• Into a less optically dense material - The ray speeds up and bends away from the normal, so the angle of refraction is larger than the angle of incidence ($r>i$).

A prism splits white light into a spectrum

• White light is a mixture of all the colours in the visible spectrum, each with a different wavelength.
• Different wavelengths refract by different amounts, so a triangular prism separates white light into a spectrum. This is called dispersion.

Why the colours disperse

• All colours travel at the same speed in air, but travel at different speeds in glass.
• Violet slows down the most and refracts the most.
• Red slows down the least and refracts the least.
• Because the sides of a triangular prism are not parallel, the colours spread out further as they leave rather than recombining.

Light of a single frequency (one colour) is called monochromatic.