i) If f=0.5m for a glass lens, what is the powerof the lens? Ii) The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. Its focal length is 12 cm. What is the refractive index of glass? Iii) A convex lens has 20 cm focal length in air. What is focal length in water? (Refractive index of air-water =1.33, refractive index for air glass=1.5)

Explanation

(a) `P = (1)/(f(m)) = (1)/(0.5) = +2D " "` (b) `(1)/(f) = (mu-1)((1)/(R_(1)) - (1)/(R_(2))) implies (1)/(12) = (mu-1)((1)/(10) - (1)/(-15)) implies mu=1.5`
(c) `(1)/(f) = (mu-1) ((1)/(R_(1)) - (1)/(R_(2))) "so" (1)/(f) alpha (mu-1), (f_(w))/(f_(a))= ((mu_(l)-1))/((._wmu_(l) -1)) implies f_(w) = ((1.5-1))/(((1.5)/(1.33) - 1))xx 20 = 78.2 "cm"`