An experimentalist devises a method for finding the radius of curvature of a convex mirror. He uses a plane mirror strip between the object and the convex mirror and adjusts it till the two virtual images formed by reflection at both the mirrors coincide without parallax. In his observations, the object distance from the convex mirror is 0.5 m while it is 0.30 m in front of the plane mirror. Find the radius of curvature (in cm) of the convex mirror.
Options

Question

An experimentalist devises a method for finding the radius of curvature of a convex mirror. He uses a plane mirror strip between the object and the convex mirror and adjusts it till the two virtual images formed by reflection at both the mirrors coincide without parallax. In his observations, the object distance from the convex mirror is 0.5 m while it is 0.30 m in front of the plane mirror. Find the radius of curvature (in cm) of the convex mirror.

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: Use the law of reflection i = r and plane-mirror symmetry. The image is as far behind the mirror as the object is in front; rotation of a mirror by φ rotates the reflected ray by 2φ. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is 25. Therefore the correct option is A.