The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is

Solution

Physics sir · 3 steps

Use the lens maker's formula, and give the two curved faces of a convex lens opposite signs.

1. Signs of the radii. Light meets the first face, which bulges out towards it, so R₁ = +10 cm. The second face bulges the other way, so R₂ = -15 cm.

   1/f = (μ - 1)(1/R₁ - 1/R₂)

2. Put in numbers. The bracket is 1/10 + 1/15 = (3 + 2)/30 = 1/6 cm⁻¹. So 1/12 = (μ - 1)/6, which gives μ - 1 = 6/12 = 0.5.
3. So. μ = 1.5, which is option (c).

The idea to keep. For a biconvex lens the two radii always have opposite signs, so in the lens maker's formula their reciprocals add. Fix the signs first, then the algebra takes one line.

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