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Q. According to diagram, fish see two image of observer first through refraction only and other due to refraction and then reflection. Distance of the images from fish are $S_{1}$ and $S_{2}$ respectively observer can also see the two images of fish, first due to refraction only and other due to reflection and then refraction. Distance of them image from observer are $S_{3}$ and $S_{4}$ respectively :-
Question
COLUMN-I COLUMN-II
(A) $S_{1}$ (P) $H\left[1 + \frac{1}{2 \mu }\right]$
(B) $S_{2}$ (Q) $H\left[\mu + \frac{1}{2}\right]$
(C) $S_{3}$ (R) $H\left[1 + \frac{3}{2} \mu \right]$
(D) $S_{4}$ (S) $H\left[\mu + \frac{3}{2}\right]$

NTA AbhyasNTA Abhyas 2020

Solution:

Due to refraction $1^{\text{st }}$ image (w.r.t. fish)
$S_{1}=\frac{H}{2}+\mu H$
due to reflection $S_{2}=\frac{H}{2}+\left(\right.H+\mu H\left.\right)$
w.r.t. (observer)
$S_{3}=\frac{H}{2 \mu }+H;S_{4}=H+\mu H+\frac{H}{2}\mu $