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 ratio of the power in the liquid to that in air is determined using the lens maker's formula and the definition of lens power, P = 1 f . The relative refractive index for air is n_ rel,a = n_g n_a = 1.5 1 = 1.5 . For a biconvex lens with R₁ = 40 cm and R₂ = -40 cm , the power in air is P_a = (n_ rel,a - 1) ( 1 R₁ - 1 R₂ ) = (0.5) ( 1 40 + 1 40 ) = 0.5 20 = 1 40 . In the liquid, n_ rel,l = n_g n_l = 1.5 1.25 = 1.2 . The power becomes P_l = (n_ rel,l - 1) ( 1 R₁ - 1 R₂ ) = (0.2) ( 1 40 + 1 40 ) = 0.2 20 = 1 100 .