Question

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

Answer 1

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

The apparent position of the object with respect to mirror should be at the centre of curvature so that the image is formed at the same position.

Since, $\frac{Realdepth}{Apparentdepth}=\frac{1}{\mu }$ (with respect to mirror)

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