For a thin prism, ₁ is the angle of deviation produced, when prism is placed in air. When the prism is immersed in water, the angle of deviation produced is ₂ . Given ( _ a _ g = 3 2 ) and ( _ a _ w = 4 3 ). The ratio ₂: ₁ is

Step-by-step solution

The angle of deviation for a thin prism is given by = ( - 1)A , where is the refractive index and A is the prism angle. In air, the refractive index of glass is _ a _ g = 3 2 , so the deviation is ₁ = ( 3 2 - 1 )A = 1 2 A . When immersed in water, the refractive index becomes _ w _ g = _ a _ g _ a _ w = 3/2 4/3 = 9 8 , yielding deviation ₂ = ( 9 8 - 1 )A = 1 8 A . The ratio is ₂ ₁ = 1/8 1/2 = 1 4 , so ₂ : ₁ = 1 : 4 . The final answer is B