Two identical objects are placed at the same distance 18 cm in front of a convex mirror and a concave mirror having equal radii of curvature 12 cm. The ratio of the sizes of the images formed by the convex mirror and the concave mirror is:
Options

Question

Two identical objects are placed at the same distance 18 cm in front of a convex mirror and a concave mirror having equal radii of curvature 12 cm. The ratio of the sizes of the images formed by the convex mirror and the concave mirror is:

Options

G1 Physics · Accepted Answer

The magnitude of focal length for both mirrors is |f| = R/2 = 6 cm. For the convex mirror: f = +6 cm, u = -18 cm. Using 1/f = 1/v + 1/u, 1/6 = 1/v - 1/18 ⇒ 1/v = 2/9 ⇒ v = 4.5 cm. Magnification magnitude: |m₁| = |v/u| = 4.5/18 = 1/4. For the concave mirror: f = -6 cm, u = -18 cm. -1/6 = 1/v - 1/18 ⇒ 1/v = -1/9 ⇒ v = -9 cm. Magnification magnitude: |m₂| = |v/u| = 9/18 = 1/2. Therefore image-size ratio is (1/4):(1/2) = 1:2 = 1/2. Correct option: C.