Q.47

A candle is placed 18 cm in front of a concave mirror to generate a real, inverted and

doubly magnified image. The radius of curvature of the concave mirror is

____________cm. (answer in integer)

Concave Mirror Radius of Curvature: Candle 18 cm Real Inverted Doubly Magnified Image Solved

Concave mirrors produce real, inverted, and magnified images when objects are placed between the focus and center of curvature. For a candle 18 cm in front of such a mirror forming a doubly magnified real inverted image, the radius of curvature is 36 cm.^[web:2]

Problem Solution

Object distance u = -18 cm (using sign convention: object distance negative). Magnification m = -2 (real, inverted, doubly magnified), so m = -\frac{v}{u} gives v = +36 cm.^[web:2]

Mirror formula \frac{1}{v} + \frac{1}{u} = \frac{1}{f} yields \frac{1}{36} + \frac{1}{-18} = \frac{1}{f}, so f = -12 cm. Radius R = 2|f| = 36 cm (integer answer).^{[web:2][web:7]}

This confirms the image forms beyond the center of curvature, consistent with object between f and R.^[web:1]

Ray Diagram Explanation

• Ray parallel to principal axis reflects through focus F (-12 cm).
• Ray through center of curvature C (-36 cm) reflects back along itself.
• Intersection at v = +36 cm produces real, inverted image twice object size.^{[web:4][web:5]}

Image Positions Table