For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm. The refractive index of the material is :

Solution

Physics sir · 3 steps

Use the lens maker's formula, and give the second radius a minus sign because the lens is biconvex.

1. Signs of the radii. In a biconvex lens the two surfaces bulge in opposite directions. Light meets the first surface with its centre ahead, so R₁ = +15 cm. The second surface has its centre behind, so R₂ = -30 cm.

   1/f = (μ - 1)(1/R₁ - 1/R₂)

2. Put in numbers. The bracket is 1/15 + 1/30 = (2 + 1)/30 = 1/10 cm⁻¹. So 1/20 = (μ - 1)/10, which gives μ - 1 = 10/20 = 0.5.
3. So. The refractive index is μ = 1 + 0.5 = 1.5, which is option (b).

The idea to keep. For a biconvex lens the two radii carry opposite signs, so their reciprocals add in the lens maker's formula. Fix the signs first, then solve for μ.

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