Question

A concave mirror of radius R is kept on a horizontal table (figure). Water (refractive index = μ) is poured into it up to a height h. Where should an object be placed so that its image is formed on itself?
Figure

Answer 1

An object be placed so that its image is formed on itself is given by $x=\frac{R-h}{\mu}$ .

Explanation:

Let the object be placed at a height x above the water surface.

A concave R-ray mirror is placed on a horizontal

It is poured into water (refractive index = μ) to a height h

The object's apparent position regarding the mirror should be in the center of curvature so that the image is created in the same position.

Since ,  

                     $\frac{\text {Real depth}}{\text {Apparent depth}}=\frac{1}{\mu}$     with respect to mirror

                                     $\frac{x}{R-h}=\frac{1}{\mu}$

                                            $x=\frac{R-h}{\mu}$

Thus, the image is formed on itself is $x=\frac{R-h}{\mu}$.