A man makes a glass lens with refractive index (n) = 1.47, disappear in a pool of liquid. The refractive index (n1) of the liquid is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → n1 = n
A transparent object is seen only because light refracts and reflects at its surface. Both effects depend on the relative refractive index of the two media. The lens maker’s formula for a lens of index n placed in a liquid of index \( n_1 \) shows this:
\( \displaystyle \frac{1}{f} = \left(\frac{n}{n_1} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
If \( n_1 = n \), the first bracket is zero, so \( 1/f = 0 \): the lens has no focusing power. Light passes through its surfaces without bending or reflecting, and the lens cannot be seen.
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. What is the refractive index of the liquid? Could the liquid be water?”
Refraction by a Lens – “… Solution The refractive index of the liquid must be equal to 1.47 in order to make the lens disappear. This means n1 = n2.”