A bi-convex lens has radius of curvature of both the surfaces same as 1 / 6 cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides (R₁ ≠ R₂), without any change in lens power then possible combination of R₁ and R₂ is :

Solution

Physics sir · 3 steps

Same glass, same power: just keep the sum 1/R₁+1/R₂ equal to 12.

1. Lens maker's formula. For a bi-convex lens, the two curvature terms add in magnitude. If the new lens is made of the same glass, (μ - 1) stays fixed, so equal power needs an equal curvature sum.

   P = (μ - 1)(1/R₁ + 1/R₂)

2. Original lens. With R = 1/6 cm on both sides, 1/R₁+1/R₂ = 6 + 6 = 12 cm⁻¹.

   Option	1/R₁+1/R₂ (in cm⁻¹)	Same power and R₁ ≠ R₂?
   (a)	3 + 7 = 10	No
   (b)	5 + 7 = 12	Yes
   (c)	3 + 3 = 6	No, and the radii are equal
   (d)	6 + 9 = 15	No

3. So. Only (b), with R₁ = 1/5 cm and R₂ = 1/7 cm, gives the same sum of 12 with unequal radii.

The idea to keep. For lenses of the same material, power depends only on 1/R₁+1/R₂. Turn each radius into its reciprocal first, then compare the sums.

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