JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Geometrical Optics

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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:

(A)-15 cm✓ Correct
(B)45 cm
(C)-45 cm
(D)15 cm

Answer: (A)

Solution

Radius of curvature

R = 30 cm

, so

f = + 15 cm

(convex mirror). Magnification

m = + \frac{1}{2}

(virtual, erect, diminished -- always positive for a real object in a convex mirror).

m = - \frac{v}{u} = \frac{1}{2} ⟹ v = - \frac{u}{2}

Mirror formula:

\frac{1}{v} + \frac{1}{u} = \frac{1}{f} ⟹ \frac{- 2}{u} + \frac{1}{u} = \frac{1}{15} ⟹ \frac{- 1}{u} = \frac{1}{15} ⟹ u = - 15 cm

Key confirmed: A.

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Single correct option

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