Question:

A plano convex lens of refractive index μ₁ and focal length f₁ is kept in contact with another plano concave lens of refractive index μ₂ and focal length f₂. If the radius of curvature of their spherical faces is R and f₁ = 2f₂, then μ₁ and μ₂ are related as :

2μ₁−μ₂=1

2μ₂−μ₁=1

3μ₂−μ₁=1

μ₁+μ₂=3

Given, 1/f₂ = 1/f₁ = (μ₁-1)(1/∞ - 1/R)
From lens makers formula,
1/f₂ = (μ₂-1)(1/R - 1/∞)
(μ₁-1)/R = (μ₂-1)/2R
2(μ₁-1) = μ₂-1
2μ₁-2 = μ₂-1
2μ₁-μ₂=1