Question

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

• A. A distance $x=\frac{R}{\mu }$ above the surface of water
• B. A distance $x=\frac{R-h}{\mu }$ above the surface of water
• C. A distance $x=\frac{h}{\mu }$ above the surface of water
• D. A distance $x=\frac{R-2h}{\mu }$ above the surface of water

Answer 1

The correct option is B A distance $x=\frac{R-h}{\mu }$ above the surface of water

Let the object be placed at a height $x$ above the surface of the water. 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, $\frac{\text{Real depth}}{\text{Apparent depth}}=\frac{1}{\mu }$ (with respect to mirror)
Now, $\frac{x}{R-h}=\frac{1}{\mu }$
$\Rightarrow x=\frac{R-h}{\mu }$