A convex lens made of glass has focal length 0.15 ~m in air. If the refractive index of glass is 3 2 and that of water is 4 3 , the focal length of lens when immersed in water is

Step-by-step solution

Given, f _ a =0.15 ~m , _ g = 3 2 , _ w = 4 3 According to Lens maker's formula 1 f =( -1) ( 1 R ₁ - 1 R ₂ ) where = _ L _ M 1 f _ a = ( _ g _ a -1 ) ( 1 R ₁ - 1 R ₂ )= ( (3 / 2) 1 -1 ) C where C= ( 1 R₁ - 1 R₂ ) or 1 f_ a = C 2 ...(i) Also, 1 f _ w = ( _ g _ w -1 ) ( 1 R ₁ - 1 R ₂ )= ( (3 / 2) (4 / 3) -1 ) C or 1 f_ W = C 8 ...(ii) From Eqs. (i) and (ii), we get f _ w f _ a = C 2 8 C =4 or aligned f _ w &=4 f _ a &=4 0.15=0.6 ~m aligned