A light ray strikes a glass slab of thickness 15 cm at an angle of incidence of 60^ . The lateral shift of the emergent ray is measured to be 5 3 cm . If the refractive index of the material of the slab is , the value of ^2 is _____.

Step-by-step solution

The lateral shift d is given by the formula: d = t (i - r) r = t ( i - i r) Substituting the given values: 5 3 = 15 ( 60^ - 60^ r) 3 3 = 3 2 - 1 2 r 1 3 = 3 2 - 1 2 r 1 2 r = 3 2 - 1 3 = 3 - 2 2 3 = 1 2 3 r = 1 3 r = 30^ Using Snell's law at the first interface: = i r = 60^ 30^ = 3 /2 1/2 = 3 Therefore, ^2 = ( 3 )^2 = 3 . Answer: 3