Question

A planoconvex lens fits exactly into a planoconcave lens. Their planar surfaces are parallel to each other. If the lenses are made of different materials of refractive indices mu₁ and mu₂ and R is the radius of curvature of the curved surface, then focal length of the combination is

• A. \( \dfrac{R}{\mu_1 - \mu_2} \)
• B. \( \dfrac{2R}{\mu_1 - \mu_2} \)
• C. \( \dfrac{R}{2(\mu_1 - \mu_2)} \)
• D. (R)/(2-(mu₁+mu₂))

Hint:

When lenses are in contact, powers add algebraically.

Answer 1

The Correct Option is A

Step 1: Power of plano lenses: P = (μ - 1)/(R)
Step 2: Net power: P = (mu₁ - 1)/(R) - (mu₂ - 1)/(R) = (mu₁ - mu₂)/(R)
Step 3: Focal length: f = (1)/(P) = (R)/(mu₁ - mu₂)