A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is ______.

Solution

Physics sir · 3 steps

The flat face has infinite radius, so only the curved face counts in the lens maker's formula.

1. Lens maker's formula. A thin lens in air has a focal length fixed by its material and its two surfaces. Where the object sits does not change it.

   1/f = (μ - 1)(1/R₁ - 1/R₂)

2. Put in numbers. With light hitting the curved face first, R₁ = +30 cm. The plane face has R₂ = ∞, so 1/R₂ = 0. Then 1/f = (1.5 - 1) × 1/30 = 0.5/30 = 1/60.
3. So. The focal length is f = 60 cm. Turning the lens around gives the same value, so the answer is 60.

The common slip: 20. Using μ in place of (μ - 1) gives 1/f = 1.5/30 and f = 20 cm, not 60.

The idea to keep. For a plano-convex lens, f = R/(μ - 1). With μ = 1.5 that is just f = 2R, whichever face the light meets first.

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