A thin convex lens is made of two materials with refractive indices n₁ and n₂, as shown in the figure. The radii of curvature of the left and right spherical surfaces are equal.
f is the focal length of the lens when n₁ = n₂ = n.
The focal length is f + Δf when n₁ = n and n₂ = n + Δn.
Assuming 0 < Δn ≪ (n − 1) and 1 < n < 2, the correct statement(s) is/are:

Question

A thin convex lens is made of two materials with refractive indices n₁ and n₂, as shown in the figure. The radii of curvature of the left and right spherical surfaces are equal.

f is the focal length of the lens when n₁ = n₂ = n.

The focal length is f + Δf when n₁ = n and n₂ = n + Δn.

Assuming 0 < Δn ≪ (n − 1) and 1 < n < 2, the correct statement(s) is/are:

G1 Physics · Accepted Answer

Derived solution: Step 1: For paraxial refraction at a spherical surface use n₂/v - n₁/u = (n₂ - n₁)/R, applying the Cartesian sign convention at each surface. Step 2: Test each statement independently using these relations and the data/figure. Step 3: The statements that satisfy the required optical conditions are A: The relation between f f and n n remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.; C: For n = 1.5, n = 10⁻³ and f =…