Question

A concave mirror is half dipped in water. Focal length of portion of mirror in the air is ${f_1}$ and focal length of mirror in water is ${f_2}$, then (Take refractive index of water$ = \dfrac{4}{3}$)
A. ${f_1} > {f_2}$
B. ${f_1} < {f_2}$
C. ${f_1} = {f_2}$
D. ${f_1} > \dfrac{4}{3}{f_2}$

Answer 1

Hint: The focus of a mirror is defined as half the distance of the center of curvature from the pole. When the mirror is dipped in water, a mirror reflects light using its polished surface. It does not depend on the medium to define its properties, unlike the lens.

Complete answer:
In a mirror, be it spherical or plain the deflection in the direction of the light is produced by the reflection which happens due to the polished smooth surface of the mirror.
The law of reflection states that the angle of incidence equals the angle of reflection, it does not depend on the refractive index of the medium.
A mirror only reflects light according to its physical structure, therefore the focus of a spherical mirror is defined at half the distance of its center of curvature from the pole of the mirror.
Therefore even if the mirror is half dipped in the water and the other half stays in the air, the angle of incidence and the angle of reflection in the respective mediums will be the same. And all the images would be focussed on the focus of the mirror, which is the same unless the curvature of the mirror is changed.

So, the correct answer is “Option C”.

Note:
Unlike mirrors, lenses depend on the refractive index in order to focus and produce images. Even the snell’s law which defines the relationship between the angle of incidence and angle of refraction creates dependability of the image formation on the refractive index of the medium. Thus the focus of a lens can change underwater or in a different medium.