# Unit 2 Section 3 Refractive Index

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## What is Refractive Index and How to Calculate it?

Refractive Index: The ratio between the speed of light in a vacuum and the speed of light in material.

n = c / cs

n = refractive index of the material

c = 3.0 x 10^8

cs = speed of light in material in ms^-1

n of air is only slightly smaller than c so is treated as = 1

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## The Law of Refraction - Part 1

• The angle of the incoming light to the normal is theta 1, called the angle of incidence.
• The angle of the refracted ray to the normal is theta 2, called the angle of refraction.

n1 x sin(theta 1) = n2 x sin(theta 2)

n1 = refractive index of material 1

theta 1 = angle of incidence of ray of material 1

n2 = refractive index of material 2

theta 2 = angle of refraction of ray of material 2

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## Law of Refraction - Part 2

As light moves across a boundary between two different materials of different optical densities, its direction changes because of its change in speed.

The direction can change in two ways:

• Towards the normal, if it passes from a less optically dense material into a more optically dense material. E.g. if n1 < n2 then theta 1 > theta 2
• Away from the normal,  if it passes from a more optically dense material into a less optically dense material. E.g. if n1 > n2 then theta 1 < theta 2
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