How far must a girl stand in front of a concave spherical mirror of radius 120 cm to see an erect image of her face four times its natural size?

To find the object distance (u), we use the mirror formula and magnification principles. For a concave mirror, the focal length (f) is half the radius of curvature (R); given R = 120 cm, f = -60 cm (using sign convention) [c2][t2]. The girl sees an erect image four times its natural size, which implies a magnification (m) of +4 [t3]. Magnification is defined as m = -v/u, so +4 = -v/u, leading to v = -4u [t1][t4]. Substituting these into the mirror formula 1/f = 1/v + 1/u [c1][t9], we get 1/(-60) = 1/(-4u) + 1/u. Simplifying the right side: 1/(-60) = (-1 + 4) / 4u = 3 / 4u. Solving for u gives 4u = -180, so u = -45 cm. Thus, the girl must stand 45 cm in front of the mirror to see the magnified erect image.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.2.4 Mirror Formula and Magnification > p. 143
2. [2] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > What you have learnt > p. 159