JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Geometrical Optics

A mirror is used to produce an image with magnification of

\frac{1}{4}

. If the distance between object and its image is 40 cm , then the focal length of the mirror is ____ .

Answer: (C)

Solution

A magnification of magnitude

\frac{1}{4}

means the image distance is a quarter of the object distance,

∣ v ∣ = \frac{1}{4} ∣ u ∣

. For a real image from a concave mirror both lie on the same side, so the object--image separation is

∣ u ∣ - ∣ v ∣ = \frac{3}{4} ∣ u ∣ = 40 cm

, giving

∣ u ∣ = \frac{160}{3} cm

and

∣ v ∣ = \frac{40}{3} cm

. The mirror relation

\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = - \frac{3}{40} - \frac{3}{160} = - \frac{3}{32}

then gives

∣ f ∣ = \frac{32}{3}

. The focal length is about

10.7 cm

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option