The focal length of a convex lens of refractive index 1.5 is 2 cm. The focal length of the lens when immersed in a liquid of refractive index 1.25 will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 cm
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 stay the same in the liquid, so only \( (n_{21}-1) \) changes and \( f\propto1/(n_{21}-1) \).
The relative refractive index in each medium is:
In air: \( n_{21}=1.5 \)
In the liquid:
\( \begin{aligned} n_{21}' &= \frac{1.5}{1.25} \\ &= 1.2 \end{aligned} \)
The focal length in the liquid then follows from the ratio:
\( \begin{aligned} \frac{f_{\mathrm{liquid}}}{f_{\mathrm{air}}} &= \frac{n_{21}-1}{n_{21}'-1} \\ &= \frac{1.5-1}{1.2-1} \\ &= \frac{0.5}{0.2} \\ &= 2.5 \end{aligned} \)
\( \begin{aligned} f_{\mathrm{liquid}} &= 2.5\times2\,\mathrm{cm} \\ &= 5\,\mathrm{cm} \end{aligned} \)