A convex lens made of glass of refractive index 1.5 will become less convergent when it is immersed in (refractive index of water = 1.33, of the oil = 1.47)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → both (1) and (2)
By the lens maker’s formula, \( \displaystyle \frac{1}{f}=(n_{21}-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \), where \( n_{21} \) is the refractive index of the glass relative to the surrounding medium. The radii do not change, so the convergence \( 1/f \) is proportional to \( (n_{21}-1) \).
The factor \( (n_{21}-1) \) in each medium is:
In air: \( n_{21}-1=0.5 \)
In water:
\( \begin{aligned} n_{21}-1 &= \frac{1.5}{1.33}-1 \\ &\approx 0.13 \end{aligned} \)
In the oil:
\( \begin{aligned} n_{21}-1 &= \frac{1.5}{1.47}-1 \\ &\approx 0.02 \end{aligned} \)
Option (1) oil — Incorrect. The statement is true. In the oil, \( (n_{21}-1) \) falls from 0.5 to about 0.02. But the lens also becomes less convergent in water, so this option alone is incomplete.
Option (2) water — Incorrect. The statement is true. In water, \( (n_{21}-1) \) falls from 0.5 to about 0.13. But the lens also becomes less convergent in the oil, so this option alone is incomplete.
Option (3) both (1) and (2) — Correct. Water (1.33) and the oil (1.47) both have a refractive index between that of air and that of the glass. In each, \( n_{21} \) stays above 1 but is smaller than 1.5. So the lens is still converging, but with a longer focal length. In water the focal length becomes about 4 times its value in air. In the oil it becomes about 25 times its value in air.
NCERT (2026-27):
Refraction by a Lens – “…
\( \displaystyle \frac{1}{f}=(n_{21}-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\quad\left(\because\ n_{21}=\frac{n_2}{n_1}\right) \)\( \qquad (9.21) \)
Equation (9.21) is known as the lens maker’s formula.”