A magician during a show makes a glass lens μ = 1.5 disappear in a trough of liquid. The refractive index of the liquid would be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.5
The focal length of a lens of glass (refractive index \( \mu_g \)) immersed in a liquid (refractive index \( \mu_l \)) is given by the lens maker’s formula:
\( \displaystyle \frac{1}{f} = \left(\frac{\mu_g}{\mu_l} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
The lens becomes invisible when it no longer bends the light at all, that is, when \( f\to\infty \). This needs \( \frac{\mu_g}{\mu_l} - 1 = 0 \):
\( \mu_l = \mu_g = 1.5 \)
With the same refractive index on both sides, light passes through the glass surfaces undeviated, and the lens cannot be seen in the liquid.
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Refraction by a Lens – …
