The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are R₁ and R₂ respectively.

Solution

Physics sir · 4 steps

The lens bends light only because it differs from its surroundings; match the two and the bending vanishes.

1. Lens maker's formula. For a lens of refractive index μₗ in a medium of index μₘ, the power depends on how different the two are.

   1/f = (μₗ/μₘ - 1)(1/R₁ - 1/R₂)

2. Put in numbers. Here μₗ = μₘ = 1.4, so μₗ/μₘ - 1 = 1 - 1 = 0. Whatever the radii are, 1/f = 0.
3. Physical picture. Light does not refract at a boundary between two media of the same refractive index. The lens behaves like a plane sheet of the medium, so rays pass straight through.
4. So. 1/f = 0 means the focal length is infinite, option (b).

The idea to keep. Always use the relative index μₗ/μₘ in the lens maker's formula. Equal indices give zero power and infinite focal length; a denser medium even flips a converging lens to diverging.

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