The distance between an object and its image formed by a spherical mirror is 30 cm. The magnification is -1/3. If the focal length is x/4 cm, find the magnitude of x.
Physics · Geometrical optics · spherical mirror
JEE Mains 2025 4 April Morning Shift

Question

The distance between an object and its image formed by a spherical mirror is 30 cm. The magnification is -1/3. If the focal length is x/4 cm, find the magnitude of x.

G1 Physics · Accepted Answer

For a mirror, m = -v/u. Given, m = -1/3. Thus, -v/u = -1/3 ⇒ v = u/3. For a real inverted image, both u and v are negative. The distance between object and image is |u-v| = 30. Since v = u/3, |u-u/3| = |2u/3| = 30 ⇒ |u| = 45 cm. Thus, u = -45 cm, v = -15 cm. Mirror formula: 1/f = 1/v + 1/u = -1/15 - 1/45 = -4/45. Therefore, f = -45/4 cm. The question asks for the magnitude of x in f = x/4 cm, so |x| = 45. Answer: 45.