3.2.7

# Refraction at a Plane Surface

Test yourself

## Refractive Index

Light changes speed and bends when it passes from one medium to the next. This is called refraction.

### Change of speed

• When light passes from one medium to the next, it changes speed.
• In a vacuum (empty space), light travels at speed c = 3×108m/s.
• Light travels more slowly in all other materials.
• The refractive index, n, of a material is the ratio of the speed of light in a vacuum, c, to the speed of light in that material, cs. It is given by:
• $n = \frac{c}{c_s}$

### Refractive index of air

• Air contains lots of chemicals and elements such as oxygen and nitrogen.
• However, the speed of light in air is so close to the speed of light in a vacuum, that we can approximate them to be the same:
• cair ≈ c
• Therefore the refractive index of air is approximately 1.

## Snell's Law

Snell's law relates refractive indices to the angles of incidence and refraction.

### Equation

• Snell's law is:
• $n_1 \sin \theta_1 = n_2 \sin \theta_2$
• The ray of light begins in the medium with refractive index n1.
• θ1 is the angle of incidence.
• n2 is the refractive index of the medium the light passes into.
• θ2 is the angle of refraction.

### Direction of bending

• When light travels from a less optically dense medium to a more optically dense medium, it bends towards the normal.
• When light travels from a more optically dense medium to a less optically dense medium, it bends away from the normal.
• The more optically dense a medium is, the slower light travels through it, and therefore the larger its refractive index.

## Critical Angle

When light travels from a medium with a high refractive index (more optically dense) to a medium with a low refractive index (less optically dense) at the critical angle, it will be entirely reflected.

### Equation

• The critical angle, θc occurs when:
• $\sin \theta_c = \frac{n_2}{n_1}$
• Where n1 is the more optically dense material and n2 is the less optically dense material.

### Total internal reflection

• At angles of incidence larger than or equal to the critical angle, no light is refracted.
• Instead, all the light is reflected.
• This is called total internal reflection.