A ray of light is incident on a surface of glass slab at an angle 45 ° . If the lateral shift produced per unit thickness is 1 3 m , then the angle of refraction produced at the incident surface is

Step-by-step solution

Here, angle of incidence i = 45 ° L a t e r a l s h i f t d T h i c k n e s s o f g l a s s s l a b t = 1 3 Lateral shift d = t sin ⁡ δ cos ⁡ r = t sin ⁡ ( i - r ) cos ⁡ r ⇒ d t = s i n ⁡ ( i - r ) cos ⁡ r or d t = sin ⁡ i cos ⁡ r - cos ⁡ i sin ⁡ r cos ⁡ r or d t = sin ⁡ 45 ° cos ⁡ r - cos ⁡ 45 ° sin ⁡ r cos ⁡ r = cos ⁡ r - sin ⁡ r 2 cos ⁡ r or d t = 1 2 1 - tan ⁡ r or 1 3 = 1 2 1 - tan ⁡ r or tan ⁡ r = 1 - 2 3 or r = tan - 1 ⁡ 1 - 2 3