FE Physics
Formulas & Explanation

Refraction

Refraction is the change in direction of a wave due to a change in its medium (light travelling from medium 1 to medium 2)

The cause is of the change in direction is the difference in speed of light in both media.

There is:

n = sin i/sin r  (Snellius’law of refraction )

i  angle of incidence  (angle between incident ray and normal )

r  angle of refraction (angle between refracted ray and normal)

n  index of refraction

Index of refraction of a material

n = (speed of light in vacuum (mostly taken as air)) / (speed of light in the material)

Example 1

Find the speed of light in glass.

nglass = 1.5

nglass =  cvac / cglass

1.5 = (3.00 x 108 )/ cglass

cglass = 2.25 x 108 m s-1

Refraction of light from an optically less dense medium to an optically more dense medium

-          refraction to the normal

-          i > r

Example 2

A ray of light travels from air to glass

The index of refraction of glass is 1.5

Angle of incidence i is 40 o.

Find the angle of refraction r

1.5 = sin 40o/sin r      1.5 sin r = sin 40o

1.5 sin r = 0.94279       sin r =0.94279/1.5 = 0.428525

r = 25o

(Except the refracted ray, there is a reflected ray. This is not shown in the figure)

Refraction of light from an optically more dense medium to an optically less dense medium

Example : glass → air

-          refraction from the normal

-          i < r

(The reflected ray is not shown in the figure)

The largest angle of incidence where refraction occurs is called ‘critical angle’ (ic )

Then the angle of refraction is 90o

(The reflected ray is not shown in the figure)

When  i > ic  the ray is totally reflected in the first medium.

This is called : total internal reflection

Example 3

Calculate the critical angle for the transition from glass to air

n glas = 1.5

This means : n air→glass = 1.5

n glass→air  =  1/n air→glass = 1/1.5 = 0.667

Law of Snellius:

sin ic/sin 90 = 0.667       sin i c = 0.667     ic = 42o