Question

A concave mirror and a converging lens have the same focal length in air. Which one of the two will have greater focal length when both are immersed in water?

Answer 1

Hint Refraction is strictly a function of a relative refractive index. So in the case of mirror and lens, both will have different focal lengths. And we also know the medium does not affect the length at some particular point. So by using all the above concepts we can answer this problem.
Formula used:
The focal length of the concave mirror will be given by
\[f = \dfrac{R}{2}\]
Here,
$f$, will be the focal length
$R$, will be the radius
The formula for the converging lens when immersed in water, will be given by
\[\dfrac{1}{{{f_w}}} = \left( {\dfrac{{{n_1}}}{{{n_2}}} - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right)\]
${f_w}$, the focal length in the water
$\dfrac{{{n_1}}}{{{n_2}}}$, will be the refractive index of the material of the lens relative to water.

Complete Step By Step Solution Reflection is independent of the refractive index and hence there will be no change in the focal length of a concave mirror even if immersed.
The focal length of a raised convex lens increments when drenched in a fluid with a refractive record lower than the focal point material. It gives the same effect as an identical convex lens in the air made with lower refractive index material.
As we know the focal length of a concave mirror is immersed in water then the focal length will not change. That is
\[f = \dfrac{R}{2}\]
And the formula for the converging lens when immersed in water.
\[\dfrac{1}{{{f_w}}} = \left( {\dfrac{{{n_1}}}{{{n_2}}} - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right)\]

So from here, we can see that the RI of the converging lens will be greater than the concave mirror when they are being immersed in the water.

Note Focal length is the distance between the lens and the point where the parallel incident rays meet (or intersect). If you want to know the terminology used in photography as in, the focal length of a lens, the simple answer to it is lesser the focal length wider will be the angle of view and smaller will be the zooming range.