A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → become infinite
The focal length of a lens in a medium follows from the lens maker’s formula, which contains the refractive index of the lens relative to the surrounding medium.
\( \displaystyle \frac{1}{f} = \left(\frac{n_{\mathrm{lens}}}{n_{\mathrm{liquid}}} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
\( n_{\mathrm{lens}} = n_{\mathrm{liquid}} \Rightarrow 1/f = (1 - 1)(\ldots) = 0 \Rightarrow f \to \infty \)
Light is not bent at either surface, so the lens behaves like a plane sheet of glass.
NCERT (2026-27):
Refraction by a Lens – “… Example 9.6 A magician during a show makes a glass lens with n = 1.47 disappear in a trough of liquid. … Solution The refractive index of the liquid must be equal to 1.47 in order to make the lens disappear. This means n1 = n2. This gives \( 1/f = 0 \) or \( f \rightarrow \infty \). The lens in the liquid will act like a plane sheet of glass.”