The back wall of an aqaurium is a mirror that is 30 cm away from the fron wall. The sides to 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 dows 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 refractive index `4//3`

Answer

(a) `33.75` cm (b) Refractive index has to increase, `(3)/(2)`

Explanation

a. The distance of `F_(1)` from the surface is 45 cm. Apparent depth of `F_(1)` from front wall is,
`x=(45)/(mu_(L))=(45)/(4//3)=33.75cm`
b. For x to decrease, `mu_(L)` has to increase.
For limiting case, `x=30cm`
So, `mu_(L) =(45)/(30)=(3)/(2)`