JEE Advanced 2026 · Paper 1 · Physics Q4

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PhysicsSingle correct+3 / -1Question 20 of 48

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index $n_L$ . The correct plot showing the variation of the power, in the units of diopter $(D)$ , as a function of $n_L$ is:

Power (D) against n_L from 1.0 to 2.0, axis −5 to 5: a curve falling from 5 at n_L = 1.0, concave up, crossing zero at 1.5 and reaching about −2.5 at 2.0.

Power (D) against n_L from 1.0 to 2.0, axis −5 to 5: a straight line falling from 5 at n_L = 1.0 through zero at 1.5 to −5 at 2.0.

Power (D) against n_L, axis −40 to 40: positive near 15 at n_L = 1.0, rising steeply to +∞ just before 1.5; beyond 1.5 it comes up from −∞ and levels off near −10 by 2.0.

Power (D) against n_L, axis −40 to 40: negative near −10 at n_L = 1.0, falling to −∞ just before 1.5; beyond 1.5 it comes down from +∞ and levels off near 15 by 2.0.

Answer and worked solution

Official answer: A

For the lens in the liquid, with $\frac1{R_1}-\frac1{R_2}=\frac2{0.2}=10\ \text{m}^{-1}$ , the focal length is
$\frac1f=\left(\frac{1.5}{n_L}-1\right)\times10.$

Two conventions for power.

$P=\dfrac1f$ : $P=10\left(\dfrac{1.5}{n_L}-1\right)$ , which is $5$ D at $n_L=1$ , $0$ at $1.5$ and $-2.5$ D at $2$ , concave up. This is graph (A).
$P=\dfrac{n_L}f$ (power measured in the medium): $P=10(1.5-n_L)$ , a straight line from $5$ D to $-5$ D. This is graph (B).

Both conventions are in use, and the official key accepts either (A) or (B).

Topics:Thin lenses and lens maker's formula

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