A concave mirror of radius of curvature h is placed at the bottom of a tank containing a liquid of refractive index `mu` upto a depth d. An object P is placed at height h above the bottom of the miror. Outside the liquid, an observer O views the object and its image in the mirror. The apparent distance between these two will be

Options

A. `h(1-(1)/(mu))`
B. `(2h)/(mu-1)`
C. zero
D. `(2h)/(mu)`

Answer

c.

Explanation

There will be two images on by direct observation other by reflection through mirror.
Apparent depth
`=("Real depth")/(mu_(rel))`
`=("Real depth")/(((mu_("incident"))/(mu_("refractive")))) =((d-h))/((mu//1))`
`d_(app)=((d-h))/(mu)`
Object P is placed at the center of curvature of the mirror. Its image will be formed at P itself.
So, for image also,
`d_(app)=((d-h))/(mu)-((d-h))/(mu)=0`