Refractive index of a glass convex lens is 1.5 . The radius of curvature of each of the two surfaces of the lens is 40 cm. The ratio of the power of the lens when immersed in a liquid of refractive index 1.25 to that when placed in air is

Step-by-step solution

The power of a lens is given by the lens maker's formula: P = 1 f = ( _ rel - 1) ( 1 R₁ - 1 R₂ ) When the lens is placed in air, the relative refractive index is _ rel = _g _a = 1.5 1 = 1.5 . The power in air is: P_a = (1.5 - 1) ( 1 R₁ - 1 R₂ ) = 0.5 ( 1 R₁ - 1 R₂ ) When the lens is immersed in the liquid, the relative refractive index is _ rel = _g _l = 1.5 1.25 = 1.2 . The power in the liquid is: P_l = (1.2 - 1) ( 1 R₁ - 1 R₂ ) = 0.2 ( 1 R₁ - 1 R₂ ) Taking the ratio of the power of the lens in the liquid to that