A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

Solution

Physics sir · 3 steps

Only the relative refractive index changes in water, so compare (μᵣₑₗ - 1) in the two media.

1. Lens maker's formula. For a lens in a medium, 1/f = (μ_g/μₘ - 1)(1/R₁ - 1/R₂). The curvature bracket stays the same, so f depends only on (μ_g/μₘ - 1).

   f_w/fₐ = (μ_g - 1)/(μ_g/μ_w - 1)

2. Put in numbers. In air, μ_g - 1 = 0.5. In water, take μ_w = 1.33 ≈ 4/3, so 1.5/(4/3) - 1 = 9/8 - 1 = 1/8. The ratio is 0.5/(1/8) = 4.
3. So. f_w = 4 × 24 cm = 96 cm, which is option (a).

The idea to keep. Put a lens in a denser medium and (μᵣₑₗ - 1) shrinks, so the focal length grows. Glass in water always gives about 4 times the air focal length.

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