Question

For the arrangement of mirrors as shown in the figure, a light ray is found to retrace its path when the angle of incidence on the plane mirror is ${30}^{\circ }$. Find the distance $OP$, if focal length of concave mirror is $25\text{cm}$.

• A. $40\text{cm}$
• B. $10\text{cm}$
• C. $50\text{cm}$
• D. $15\text{cm}$

Answer 1

The correct option is C $50\text{cm}$

The light ray will retrace its path, if the ray incident on the concave mirror after getting reflected from the plane mirror is along the normal to the concave mirror.
The normal of a spherical mirror cuts principle axis at centre of curvature.
Thus, $P$ is the centre of curvature.

So, radius of curvature,
$OP=2f$
$\Rightarrow OP=2\times 25=50\text{cm}$