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A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is

Asked in JEE Main 29th Jan 1st Shift 2024 · Mirror formula and magnification

(1) 45 cm
(2) -15 cm
(3) -45 cm
(4) 15 cm

Answer: (2) -15 cm

Step-by-step solution

f=+15 cm, m=+1/2 (virtual erect image).

m=f/(f-u): (15)/(15-u)=1/2

15-u=30, u=-15 cm

Why the other options are wrong

(1) Uses m=-1/2 (inverted image) and drops the sign.
(3) Uses m=-1/2 (a real inverted image, which a convex mirror cannot form), gets |u|=45 cm and attaches the real-object sign.
(4) Drops the sign convention; a real object has negative u.

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