Question

A concave mirror of focal length $f$ and diameter $d(d<<f)$ is kept horizontally and filled with water. Rays of light parallel to the mirror axis are incident on it. After reflection, the rays will focus close to

• A. 0.25f
• B. 1.33f
• C. f
• D. 0.75f

Answer 1

Answer: (B)

1.33f

The correct option is (D).

The focal length of the given Plano-convex lens is

$\frac{1}{f_L}=\left(\mu -1\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right]=\left(\frac{4}{3}-1\right)\left[\frac{1}{\infty }-\frac{1}{\left(-2f\right)}\right]$

$f_L=6f$

Now the equivalent Power is given as combination power $P_L$ of lens and $P_m$ of mirror, hence

$P_{eq}=2P_L+P_m=2\left(\frac{1}{6f}\right)+\frac{1}{f}=\frac{4}{3f}$

Hence,

$\therefore f_{eq}=\frac{3f}{4}=1.33f$