A person wants a real image of his own, 3 times enlarged. Where should he stand

A person wants a real image of his own, 3 times enlarged. Where should he stand in front of a concave mirror of radius of curvature of 30 cm?

(a) 90 cm
(b) 10 cm
(c) 20 cm
(d) 30 cm

20 cm

Given, m = -3 and R = 30 cm

f = -(R / 2) = -15 cm

We know that, m = -(v / u) ⇒ -3 = -v / u

Therefore, v= 3u

1/f = (1/v) + (1/u) ⇒ (1/-15) = (1/3u) + (1/u) = (1+3) / 3u

-3u = 4 × 15

u = (-4 × 15) / 3

Initial position of a person, u = -20 cm

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