A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R=14 ~cm . For this bi-convex lens, for an object distance of 40 ~cm , the image distance will be

Step-by-step solution

According to lens maker's formula 1 f =(n-1) ( 1 R₁ - 1 R₂ ) For the first lens : n=1.5, R₁=+14 ~cm , R₂= 1 f₁ =(1.5-1) ( 1 14 - 1 )= 0.5 14 For the second lens : n=1.2, R₁= , R₂=-14 ~cm 1 f₂ =(1.2-1) ( 1 - 1 -14 )= 0.2 14 The focal length of the bi-convex lens is 1 f = 1 f₁ + 1 f₂ = 0.5 14 + 0.2 14 = 0.7 14 = 1 20 According to thin lens formula; 1 v - 1 u = 1 f 1 v - 1 -40 = 1 20 or v=40 ~cm