A biconvex lens made of a material with refractive index 1.6 has a focal length of 20 cm in air. If the radii of curvature of its two surfaces are in the ratio 1 : 2 , the value of the smaller radius of curvature is :

Step-by-step solution

Let the radii of curvature of the biconvex lens be R₁ = +R and R₂ = -2R , where R is the smaller radius. According to the lens maker's formula: 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) Substituting the given values: 1 20 = (1.6 - 1) ( 1 R - 1 -2R ) 1 20 = 0.6 ( 1 R + 1 2R ) 1 20 = 0.6 3 2R 1 20 = 0.9 R R = 20 0.9 = 18 cm Answer: 18 cm