A thin convex lens is made of two materials with refractive indices n 1 and n 2 , as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n 1 = n 2 = n . The focal length is f + Δ f when n 1 = n and n 2 = n + Δ n . Assuming Δ n n - 1 and 1 n 2 , the correct statement(s) is/are:

Step-by-step solution

Given that the lens is made of two plano-convex lenses. Let it be L 1 or L 2 . Let focal length of L 1 = f 1 , An focal length of L 2 = f 2 ∴ Using lens maker's formula, 1 f 1 = n 1 - 1 1 R - 1 ∞ , and 1 f 2 = n 2 - 1 1 ∞ - 1 - R ⇒ 1 f 1 = n 1 - 1 R ⇒ 1 f 2 = n 2 - 1 R Now, for the first situation, given that, n 1 = n 2 = n and focal length of combination is ‘ f ’ ⇒ 1 f = 1 f 1 + 1 f 2 = 2 n - 1 R ....(1) In the second situation, n 1 = n , n 2 = n + Δ n and focal length= f + Δ f ⇒ 1 f + Δ f = n - 1 R + n + Δ n - 1