When a convex lens of glass is immersed in water, its power will

The correct answer is Option (2) → decrease

By the lens maker's formula, the power of a lens depends on the refractive index of the glass relative to the surrounding medium.

    \( \displaystyle P = \frac{1}{f} = \left(\frac{n_g}{n_m} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)

Taking \( n_g = 1.5 \) and \( n_w = 1.33 \), the first bracket in air and in water is:

    \( n_g/n_{\mathrm{air}} - 1 = 1.5 - 1 = 0.5 \)
    \( n_g/n_w - 1 = 1.5/1.33 - 1 \approx 0.13 \)

The bracket containing the radii is unchanged, so the power falls to about a quarter of its value in air. It decreases, but it stays positive because glass is still denser than water.

Option (1) increase — Incorrect. The relative refractive index falls in water, so the power cannot increase.

Option (2) decrease — Correct. \( n_g/n_w - 1 \) is smaller than \( n_g - 1 \), so the power decreases.

Option (3) remain the same — Incorrect. The power would stay the same only if the surrounding medium had the same refractive index as air.

Option (4) become zero — Incorrect. The power becomes zero only when the medium has the same refractive index as the glass; water's index (1.33) is less than 1.5.

NCERT (2026-27):
Power of a Lens – “… Clearly, a lens of shorter focal length bends the incident light more, while converging it in case of a convex lens and diverging it in case of a concave lens.”

Power of a Lens – “… Example 9.7 … (iii) A convex lens has 20 cm focal length in air. What is focal length in water? (Refractive index of air-water = 1.33, refractive index for air-glass = 1.5.)”

Power of a Lens – “… Combining these two equations, we find f = + 78.2 cm.”