Question

Assertion A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length.
Reason The refractive index of water is smaller than the refractive index of air.

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. Assertion is true but reason is false
• D. Both assertion and reason are false

Answer 1

Answer: (D)

If a mirror is placed in a medium other than air, its focal length does not change as $ f = \frac{R}{2}$. But for the lens
$ \frac{1}{f_a} = (_a n _g - 1) \bigg(\frac{1}{R_1}-\frac{1}{R_2}\bigg)$
and $ \frac{1}{f_w} = (_w n _g - 1) \bigg(\frac{1}{R_1}-\frac{1}{R_2}\bigg)$
As $ _w n _g < _a n _g, $ hence focal length of lens in water increase.
The refractive index of water is $\frac{4}{3}$ and that of air is 1.
Hence, $ \mu_w > \mu_a . $