JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Geometrical Optics

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Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

(A) $1/2$ ✓ Correct
(B)2
(C)3
(D) $1/3$

Answer: (A)

Solution

For both mirrors

R = 12

cm, so

f = \frac{R}{2} = 6

cm, with the object at

u = - 18

cm. For the concave mirror (

f = - 6

cm),

\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = - \frac{1}{6} + \frac{1}{18} = - \frac{1}{9}

, so

v = - 9

cm and

∣ m_{c} ∣ = \frac{v}{u} = \frac{9}{18} = \frac{1}{2}

. For the convex mirror (

f = + 6

cm),

\frac{1}{v} = \frac{1}{6} + \frac{1}{18} = \frac{2}{9}

, so

v = 4.5

cm and

∣ m_{c x} ∣ = \frac{4.5}{18} = \frac{1}{4}

. The ratio of the image size by the convex mirror to that by the concave mirror is

\frac{1/4}{1/2} = \frac{1}{2}

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Geometrical Optics

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