Question

Given the angle of incidence and the angle of refraction, in a material of index of refraction n, find the speed of light in the material.

Answer 1

Solution -

• Angle of incidence = i
• Angle of refraction = r
• Refractive index of medium 1  ( rarer than 2) with respect to air = n₁
• Refractive index of medium 2 ( denser than 1) with respect to air = n₂
• Velocity of light in medium 1 = V₁
• Velocity of light in medium 1 = V₂

Suppose the light is travelling from medium 1 to medium 2

Relation between i , r , n and V

n₂ / n₁ = sin i / sin r = V₂  / V₁

suppose the light is travelling from air means we consider medium 1 is air means n₁ = 1

V₁ = C  ( Speed of the light )

putting this values in above equation -

n₂ =     sin i / sin r   =   V₂  / C

From these equations on comparing we get -

V₂   = C n₂ , or

V₂   = [ sin i / sin r ] x C

These are the expression for velocity in terns of the refractive index and angles .

Please rate good if you feels satisfied with the solution ,

Thank you.