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: (a). Take light going down; both surfaces have centre of curvature above, so R₁ = -|R₁|, R₂ = -|R₂|. Glass: Pg = 1/2(-(1)/(|R₁|) + (1)/(|R₂|)) Top water (plano-convex): (1)/(3|R₁|); bottom water (plano-concave): -(1)/(3|R₂|). P = (1/3 - 1/2)(1)/(|R₁|) + (1/2 - 1/3)(1)/(|R₂|) = -1/6((1)/(|R₁|) - (1)/(|R₂|)) So the answer is (a).

In the diagram given below, there are three lenses formed… | JEE Main 2025 (22 Jan, Shift 1)

Q20JEE Main 2025 · 22 JAN · SHIFT 1Medium

Combination of Lenses

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $|R_1|$ and $|R_2|$ , i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is

Show answer and solution

Answer: (a)

Take light going down; both surfaces have centre of curvature above, so $R_1 = -|R_1|$ , $R_2 = -|R_2|$ .
Glass: $P_g = \frac{1}{2}\left(-\frac{1}{|R_1|} + \frac{1}{|R_2|}\right)$
Top water (plano-convex): $\frac{1}{3|R_1|}$ ; bottom water (plano-concave): $-\frac{1}{3|R_2|}$ .
$P = \left(\frac{1}{3} - \frac{1}{2}\right)\frac{1}{|R_1|} + \left(\frac{1}{2} - \frac{1}{3}\right)\frac{1}{|R_2|} = -\frac{1}{6}\left(\frac{1}{|R_1|} - \frac{1}{|R_2|}\right)$
So the answer is (a).

Report a mistake

Combination of Lenses question from JEE Main 2025 (22 Jan, Shift 1)

More questions on Combination of Lenses