JEE Main 2025 · 22 January · morning · Single correct · +4 / −1
In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to |R₁| and |R₂|, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is
- (a) -1/6(1/|R₁|-1/|R₂|)
- (b) -1/6(1/|R₁|+1/|R₂|)
- (c) 1/6(1/|R₁|+1/|R₂|)
- (d) 1/6(1/|R₁|-1/|R₂|)
Answer and solution
Answer (a) -1/6(1/|R₁|-1/|R₂|)
Solution
Physics sir · 3 steps
Split it into three thin lenses in contact and add their powers, keeping the signs of the radii straight.
- Fix the signs. Let light travel downward and take downward as positive. Both curved surfaces bulge downward, so their centres of curvature lie above them. That makes R₁ = -|R₁| and R₂ = -|R₂|, and the flat faces have R = ∞.
- Lens maker formula. For each lens, P = (μ - 1)(1/Rₜₒₚ - 1/R_(bottom)). The water has μ - 1 = 1/3 and the glass has μ - 1 = 1/2.
Lens Top face, bottom face Power Upper water (plano-convex) ∞, -|R₁| 1/3(0 + 1/|R₁|) = +1/3|R₁| Glass (meniscus) -|R₁|, -|R₂| 1/2(-1/|R₁| + 1/|R₂|) Lower water (plano-concave) -|R₂|, ∞ 1/3(-1/|R₂| - 0) = -1/3|R₂| P = 1/|R₁|(1/3 - 1/2) + 1/|R₂|(1/2 - 1/3) = -1/6(1/|R₁| - 1/|R₂|)
- So. Thin lenses in contact add their powers, and the total is -1/6(1/|R₁| - 1/|R₂|), which is option (a). This is positive because the lower surface is more curved (|R₂| < |R₁|), so the combination converges.
The idea to keep. Thin lenses in contact just add their powers. Fix one direction for the light, give every radius its sign once, and remember that flat faces contribute nothing.
Answer from the NTA final answer key. Solution by PrepWiser.