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

Given,
A concave mirror of radius 'R' kept on a horizontal table.
'h' is height up to which the water is poured into the concave mirror.
Let the object be placed at height 'x' above the surface of water.
We know if we place the object at the centre of curvature of the mirror, then the image itself will be formed at the centre of curvature.
Therefore, the apparent position of the object with respect to the mirror should be at the centre of curvature so that the image is formed at the same position.



Since,
$\frac{\mathrm{Real}\mathrm{depth}}{\mathrm{Apparent}\mathrm{depth}}=\frac{1}{\mu }$
(with respect to mirror)
$$\begin{gathered} \mathrm{Now},\frac{x}{R\mathit{-}h}\mathit{=}\frac{\mathit{1}}{\mu } \\ \mathit{\Rightarrow }\mathit{}x\mathit{=}\frac{R\mathit{-}h}{\mu } \end{gathered}$$
Hence, the object should be placed at $\frac{R-h}{\mathrm{\mu }}$ above the water surface.