The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index =1.7 ) are same. If the curvature of planoconcave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ____

Solution

Physics sir · 4 steps

Write both powers with the lensmaker formula; the shared radius R₂ links them and the ratio drops out.

1. Biconvex lens. Call the front radius R₁ and the back radius R₂. With μ = 1.5, its power is P₁ = (1.5 - 1)(1/R₁ + 1/R₂) = 0.5(1/R₁ + 1/R₂).
2. Plano-concave lens. Its curved face has the same radius R₂, and the flat face contributes 1/∞ = 0. With μ = 1.7, the magnitude of its power is |P₂| = 0.7/R₂.

   0.5(1/R₁ + 1/R₂) = 0.7/R₂

3. Solve the ratio. Move the R₂ term to the right: 0.5/R₁ = (0.7 - 0.5)/R₂ = 0.2/R₂. So R₁/R₂ = 0.5/0.2 = 5/2.
4. So. The front and back radii of the biconvex lens are in the ratio 5 : 2, which is option (b).

The idea to keep. When two lenses share a surface, write each power with the lensmaker formula using the same R. A flat face adds nothing. Equate magnitudes first, and only then think about signs.

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