Question

The back wall of an aquarium is a mirror that is $30cm$ away from the front wall. The sides of the tank are negligibly thin. A fish is swimming midway between the front and back walls.
a. An image of the fish appears behind the mirror. How far does this image appear to be from the front wall of the aquarium?
b. Would the refractive index of the liquid have to be larger or smaller in order for the image of the fish to appear in front of the mirror, rather than behind it? Find the limiting value of this refractive index. Initially, water is there in aquarium having a refractive index $4/3$.

Answer 1

The distance of $F_1$ from the surface is $45cm$. Apparent depth of $F_1$ from front wall is,
$x=\frac{45}{{\mu }_L}=\frac{45}{4/3}=33.75cm$
b. For $x$ to decrease, ${\mu }_L$ has to increse.
For limiting case, $x=30cm$
So, ${\mu }_L=\frac{45}{30}=\frac{3}{2}$.