The power of a lens (biconvex) is 1.25 m⁻¹ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium:

Solution

Physics sir · 4 steps

Use the lens maker's formula with the relative index μₗ/μₘ, then solve for the medium.

1. Relative index. Inside a medium, the lens bends light by how much denser it is than its surroundings. So the lens maker's formula uses μₗ/μₘ in place of μₗ.

   P = 1/f = (μₗ/μₘ - 1)(1/R₁ - 1/R₂)

2. Curvature term. For a biconvex lens, R₁ = +0.2 m and R₂ = -0.4 m. So 1/R₁ - 1/R₂ = 5 + 2.5 = 7.5 m⁻¹.
3. Solve for medium. 1.25 = (1.5/μₘ - 1) × 7.5, so 1.5/μₘ - 1 = 1/6. That gives 1.5/μₘ = 7/6.
4. So. μₘ = (1.5 × 6)/7 = 9/7, which is option (b).

The idea to keep. A lens in a medium works with the relative index μₗ/μₘ. The closer the medium's index is to the lens's, the weaker the lens becomes.

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