Question

Water- mirror system is shown in figure. $A$ point object $P$ is also marked. The radii of curriature of mirror is $120cm$. Two images of object $P$ are considered one by direct reflection from water surface and other by refraction at water surface-reflection at mirror-refraction at water surface. The separation between two images is

Refractive index of water is $\frac{48}{3}$

• A. $36$ cm
• B. $12$ cm
• C. $24$ cm
• D. $48$ cm

Answer 1

The correct option is C

$24$ cm

Ist Image
It is formed due to reflection at water surface, (which can be considered as plane mirror) so depth of I, from surface of water is $12cm$
list image
ray diagram for this situation is shown in figure here $I_2$ is the final image. for refraction at water surface, $O{P}_1={\mu }_{\omega }\times 12=16cm$
for reflection at convex mirror,
$\frac{1}{Q{P}_2}+\frac{1}{-(24+16)}=\frac{1}{60}$$\Rightarrow Q{P}_2=24cm$
for $2^{nd}$ refraction at water surface,
$O{P}_3=\frac{24+24}{\frac{4}{3}}=36cm$
here ray diagrame is not to scale
Required seperation $36-12=24cm$