Question

A spherical mirror is placed $10 \, cm$ below the level of water. A point object is placed in air $30 \, cm$ above the water surface on the axis of the mirror such that two images seen by an observer above the water surface coincide. The images are formed by partial reflection at the water surface and due to emerging light after reflection from the mirror. Find the focal length of the mirror. ( $\mu _{\text{water}}=\frac{4}{3}$ )

• A. $\frac{1 0 0}{3}\,cm$
• B. $75 \, cm$
• C. $\frac{1 1 0}{8}\,cm$
• D. $50\,cm$

Answer 1

Answer: (B)

For partial reflection, the final image should be $30 \,cm$ below water surface i.e. $20 \,cm$ below the mirror.
For the image $30 \, cm$ below surface, its actual depth should be $h =30 \frac{4}{3}=40 \,cm$ below surface i.e. $30 cm$ below the mirror
For mirror, $u =-10+30 \frac{4}{3}$
$\Rightarrow u =-50 \,cm$ and $v =30 cm$
$\frac{1}{ f }=-\frac{1}{50}+\frac{1}{30}=\frac{-3+5}{150}=\frac{2}{150}$
or $f =75 \,cm$
convex mirror of focal length $75 \, cm$.
(diagram drawn was just for reference actually it should be a convex mirror but it was not known so we assumed concave but at final calculation, we found focal length +ve so it must be a convex mirror)