# 5.13 Refraction & Refractive Index

## Refraction & Refractive Index

• Refraction occurs when light passes a boundary between two different transparent media
• At the boundary, the rays of light undergo a change in direction and a change in speed
• The change in direction is caused by the change in speed
• Entering a more dense medium slows the light down and it bends towards the normal
• In the denser medium there are more particles closer together providing more friction to the passing of the light through the material
• Entering a less dense medium speeds the light up and it bends away from the normal
• When passing along the normal (perpendicular) the light does not change speed or direction

Refraction of light through a glass block

#### Calculating Refractive Index

• The refractive index, n, is a property of a material which measures how much light slows down when passing through it

• Where:
• c = the speed of light in a vacuum (m s–1)
• v = the speed of light in a substance (m s–1)

• Light travels at different speeds within different substances depending on their refractive index
• A material with a high refractive index is called optically dense, such material causes light to travel slower

• Since the speed of light in a substance will always be less than the speed of light in a vacuum, the value of the n is always greater than 1
• In calculations, the refractive index of air can be taken to be approximately 1
• This is because light does not slow down significantly when travelling through air (as opposed to travelling through a vacuum)

#### Snell's Law

• Snell’s law relates the angle of incidence to the angle of refraction, it is given by:

n1 sin θ1 = n2 sin θ2

• Where:
• n1 = the refractive index of material 1
• n2 = the refractive index of material 2
• θ1 = the angle of incidence of the ray in material 1 (°)
• θ2 = the angle of refraction of the ray in material 2 (°)

Snell's Law is used to find the refractive indices or the angles to the normal at a boundary

• θ1 and θ2 are always taken from the normal
• Material 1 is always the material in which the ray goes through first
• Material 2 is always the material in which the ray goes through second

#### Worked example

A light ray is directed at a vertical face of a glass cube. The angle of incidence at the vertical face is 39° and the angle of refraction is 25° as shown in the diagram. Show that the refractive index of the glass is about 1.5.

#### Exam Tip

Always double-check if your calculations for the refractive index are greater than 1. Otherwise, something has definitely gone wrong in your calculation!

The refractive index of air will not be given in the question. Always assume that nair = 1.

Always check that the angle of incidence and refraction are the angles between the normal and the light ray. Remember the normal line is not really there - it has been drawn in to give you a place to measure from.

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