Curved surfaces of a plano-convex lens of refractive index μ₁ and a plano-concave lens of refractive index μ₂ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

Solution

Physics sir · 3 steps

Treat it as two thin lenses in contact and add their powers. The common R comes out as a factor.

1. Convex part. The μ₁ piece has one flat face and one convex face of radius R. The lens maker's formula gives 1/f₁ = (μ₁ - 1)/R, a positive (converging) power.
2. Concave part. The μ₂ piece has the same curved surface, but it is hollowed in, so it diverges. Its power is 1/f₂ = -(μ₂ - 1)/R.

   1/f = 1/f₁ + 1/f₂ = ((μ₁ - 1) - (μ₂ - 1))/R = (μ₁ - μ₂)/R

3. So. Multiply both sides by R: R/f = μ₁ - μ₂. That is option (b).

The idea to keep. For lenses in contact, add the powers 1/f, with a minus sign for the diverging one. When the curved faces share the same R, the -1 terms cancel and only the difference in refractive index remains.

Answer from the NTA final answer key. Solution by PrepWiser.