An equilateral prism is immersed in a transparent liquid of refractive index 2 . The angle of minimum deviation for the prism in this liquid is found to be 30^ . When the same prism is taken out and placed in air, its angle of minimum deviation becomes D . The value of D (in degrees) is ________.

Step-by-step solution

For the equilateral prism, the angle of the prism A = 60^ . When immersed in the liquid, the relative refractive index of the prism with respect to the liquid is _ rel = _p _l , where _l = 2 and the minimum deviation is D_m = 30^ . Using the prism formula: _p _l = ( A + D_m 2 ) ( A 2 ) _p 2 = ( 60^ + 30^ 2 ) ( 60^ 2 ) = 45^ 30^ _p 2 = 1/ 2 1/2 = 2 _p = 2 2 = 2 When the prism is placed in air, let the new angle of minimum deviation be D . Applying the prism formula again: _p = ( A + D 2 ) ( A 2 ) 2 = ( 60^ + D 2 ) 3