Refraction
• Refraction happens when light changes speeds and/or is bent (traveling to different medium)

Refractive Index (n) measure of the bending of a ray of light when passing from one medium into another.
measure of the reduction in the velocity of light in the medium.

𝑛
1 sin 𝜃
1
= 𝑛
2 sin 𝜃
2 𝑛
1 𝑐
1
= 𝑛
2 𝑐
2 𝑛
1 𝑛
2
= sin 𝜃
2 sin 𝜃
1 𝑛
1 𝑛
2
= 𝑐
2 𝑐
1 𝑛
1 𝑛
2
= sin 𝜃
2 sin 𝜃
1
= 𝑐
2 𝑐
1

𝑛
1
AIR (incident ray) sin 𝜃
1
= 𝑛
2 sin 𝜃
2
Medium(refracted ray) 𝑛 𝑎𝑖𝑟 sin 𝑖 = 𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 sin 𝑟
1 ∙ sin 𝑖 = 𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 sin 𝑟 𝑛 𝑚𝑒𝑑𝑖𝑢𝑚
= sin 𝑖 sin 𝑟

Example 𝑛
1 sin 𝜃
1
= 𝑛
2 sin 𝜃
2
Calculate the angle of refraction in the glass.
1 ∙ sin 60° = 1.52 ∙ sin 𝑟 sin 𝑟 = sin 60°
1.52
sin 𝑟 = 0.570
𝑟 = 𝑠𝑖𝑛 −1 (0.570) 𝑟 = 35°

Values of refractive index for different media

Calculate the speed of light entering a diamond from the air:
(speed of light in vacuum/air : 3x10 8 ms -1
Diamond (n=2.42) 𝑛
1 𝑛
2
= sin 𝜃
2 sin 𝜃
1
= 𝑐
2 𝑐
1 n = 1
Air n = 2.42
Diamond 𝑛 𝑛
1
2
= 𝑐
2 𝑐
1
1
2.42
= 𝑐
2
3 × 10 8 𝑐
2
=
3 × 10 8
2.42
= 1.24 × 10 8 𝑚𝑠 −1

Total Internal Reflection
• Total internal reflection occurs when the angle of incidence is greater than the critical angle

Critical angle
 The angle of incidence for which the angle of refraction is 90°

Critical angle 𝑛
1 sin 𝜃
1
= 𝑛
2 sin 𝜃
2
1 ∙ sin 90° = 𝑛
2 sin 𝜃 𝑐 𝑛
2
= sin 90° sin 𝜃 𝑐 𝑛
2
1
= sin 𝜃 𝑐 sin 𝜃 𝑐
1
= 𝑛
2