A glass prism of refracting angle 60^ and refractive index 1.5 is completely immersed in a transparent liquid. The angle of minimum deviation for a parallel beam of light passing through the prism in this liquid is found to be 30^ . The refractive index of the liquid is:

Step-by-step solution

When the prism is immersed in a liquid, the relative refractive index of the glass with respect to the liquid is given by: _ rel = _ g _ l = ( A+ _ m 2 ) ( A 2 ) Given: Refracting angle A = 60^ Angle of minimum deviation _ m = 30^ Refractive index of glass _ g = 1.5 = 3 2 Substituting the angles into the formula: _ rel = ( 60^ +30^ 2 ) ( 60^ 2 ) _ rel = (45^ ) (30^ ) = 1 2 1 2 = 2 Now, using _ rel = _ g _ l : 2 = 1.5 _ l _ l = 1.5 2 = 3 2 2 Answer: 3 2 2