Immersed Lens Lab — the power of a lens in a liquid — JEE Advanced 2026 Paper 1 Q.4

01The question

Q.4 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:

(A)
(B)
(C)
(D)

The four plots are redrawn from the paper.

02The experiment

Answer— Press START: the run changes the liquid and draws the power as it goes.

Ready.

Speed

Liquid

Liquid index n_L1.00

03Detailed solution

Answer: —. The official key accepts both. They are the same lens, with "power" defined two ways.

Each surface refracts by the index difference. A spherical surface of radius R between media n₁ → n₂ has power (n₂ − n₁)/R. For the double convex lens (R₁ = +20 cm, R₂ = −20 cm) in a liquid n_L:
first surface: (1.5 − n_L)/(+0.20 m), second surface: (n_L − 1.5)/(−0.20 m), each = 5(1.5 − n_L) D.
Optical power (the surfaces added).
n_L/f = 10(1.5 − n_L) D: a straight line from 5 D (n_L = 1) through 0 (1.5) to −5 D (2.0) → (B).
Focal length in the liquid (lens-maker's formula). Divide by n_L:
1/f = (1.5/n_L − 1)(1/R₁ − 1/R₂) = 10(1.5/n_L − 1) D.
Taking the power as 1/f gives a curve (a hyperbola, bending upwards): 5 D, 0, −2.5 D at n_L = 1, 1.5, 2 → (A).
What the experiment showed. At n_L = 1.5 there is no index difference, so no refraction. The lens vanishes, f = ∞ and the power is 0 under both definitions. Above 1.5 the difference changes sign, and the double convex lens diverges the light (negative power).
Why (C) and (D) are wrong. They shoot off to ±∞ at n_L = 1.5. The focal length does that; the power goes smoothly through zero there.

n_L	f in the liquid	1/f	n_L/f
1.00 (air)	20 cm	5.00 D	5.00 D
1.33 (water)	78.2 cm	1.28 D	1.70 D
1.50	∞	0	0
2.00	−40 cm	−2.50 D	−5.00 D

Every option

Option	Plot	Verdict
(A)	curve: 5 → 0 at 1.5 → −2.5 D	Power taken as 1/f (the lens-maker's formula in the liquid). Accepted.
(B)	straight line: 5 → 0 at 1.5 → −5 D	Power taken as n_L/f, the sum of the surface powers. Accepted.
(C)	+∞ below 1.5, −∞ above	The power does not diverge at 1.5; it is zero there. Wrong under both definitions.
(D)	−∞ below 1.5, +∞ above	It diverges, and it also has the wrong sign in air, where a double convex lens converges. Wrong.

Understand the concept

A lens bends light only because its index differs from its surroundings. Its power is set by (n_glass − n_surroundings). The same double convex lens is converging in air, invisible in a liquid of its own index, and diverging in a denser liquid. "Power" in a medium is written two ways. The optical power n_L/f is the sum of the surface powers and is linear in n_L. The reciprocal of the focal length, 1/f, is that divided by n_L. In air (n_L = 1) the two agree. This is why the official key accepts (A) or (B). MathonGo's solution uses 1/f and gives (A).

Key takeaways

Lens-maker's formula in a medium: 1/f = (n_g/n_L − 1)(1/R₁ − 1/R₂).
Power is zero, and f infinite, when n_L = n_g: the lens vanishes.
For n_L > n_g, a convex lens diverges and a concave lens converges.
Optical power n_L/f is linear in n_L; 1/f is a hyperbola. Both fall through zero at n_L = n_g.
A plot that blows up at n_L = n_g is a focal length, not a power.

Verification: an independent derivation, a sympy route, an exact Snell's-law ray trace through the two spherical surfaces, and the page's own engine run by tests/verify_p1phyq04.py. The official key is "A or B", and MathonGo's solution gives (A) with the 1/f definition. Status: script-verified by the PrayogX simulation factory; no review by a person has been recorded. Liquids above about n = 1.8 are rare; the range up to 2.0 follows the question.

How to use this simulation

Press ▶ START EXPERIMENT. The liquid in the tank changes from air (1.00) to n_L = 2.00, pausing at water, 1.50 and 2.00.
Watch the laser rays: they converge, pass straight when the lens vanishes at 1.50, then diverge.
The plotter beside the tank draws both powers as the liquid changes: 1/f in blue (a curve) and n_L/f in orange (a line).
Drag n_L or tap a Liquid button to set one liquid, and read f and both powers on the scene.
Replay runs it again. Reset returns to air. Classroom fills the screen for a projector.