A container is filled with water (\( \mu=1.33 \)) up to a height of 33.25 cm. A concave mirror facing the water is placed 15 cm above the water level. An object lies at the bottom of the container. Seen from above, the image formed by the mirror coincides with the apparent position of the object. The focal length of the mirror is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 cm
Seen from above, an object under water appears raised. It appears at its apparent depth, which is the real depth divided by \( \mu \). A concave mirror forms the image back at the object itself only when the object is at its centre of curvature. Rays from there strike the mirror normally and retrace their path.
The apparent depth of the object is:
\( \begin{aligned} d_{\mathrm{app}} &= \frac{d}{\mu} \\ &= \frac{33.25\,\mathrm{cm}}{1.33} \\ &= 25\,\mathrm{cm} \end{aligned} \)
From the figure, the mirror is 15 cm above the water level. So the distance of the apparent position of the object from the mirror is:
\( \begin{aligned} R &= 15\,\mathrm{cm}+25\,\mathrm{cm} \\ &= 40\,\mathrm{cm} \end{aligned} \)
This distance is the radius of curvature, so the focal length is:
\( \begin{aligned} f &= \frac{R}{2} \\ &= \frac{40\,\mathrm{cm}}{2} \\ &= 20\,\mathrm{cm} \end{aligned} \)