JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Geometrical Optics

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A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is

(A)30
(B)45
(C) $\frac{60}{7}$
(D)15✓ Correct

Answer: (D)

Solution

Thin lenses in contact combine as

\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}} = \frac{1}{30} + \frac{1}{- 20} = - \frac{1}{60}

, so

f = - 60 cm

. With the object at

u = - 20 cm

, the lens formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

gives

\frac{1}{v} = - \frac{1}{60} - \frac{1}{20} = - \frac{1}{15}

, hence

v = - 15 cm

. The image forms at a distance of

15 cm

from the lens system.

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

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