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Question: A ray of light falls on the surface of a spherical glass paper weight making an angle \(\alpha\) w...

A ray of light falls on the surface of a spherical glass paper weight making an angle α\alpha with the normal and is refracted in the medium at an angle β\beta. The angle of deviation of the emergent ray from the direction of the incident ray is

A

(α−β)( \alpha - \beta )

B

2(α−β)2 ( \alpha - \beta )

C

(α−β)/2( \alpha - \beta ) / 2

D

(α+β)( \alpha + \beta )

Answer

2(α−β)2 ( \alpha - \beta )

Explanation

Solution

From figure it is clear that △OBC\triangle O B C is an isosceles triangle,

Hence ∠OCB=β\angle O C B = \beta and emergent angle is α\alpha

Also sum of two in terior angles = exterior angle

∴\therefore δ=(α−β)+(α−β)=2(α−β)\delta = ( \alpha - \beta ) + ( \alpha - \beta ) = 2 ( \alpha - \beta )