JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Geometrical Optics

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Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens.

Answer: 100

Solution

Rays from a distant object reach the first lens parallel to the axis, so the first lens forms an image at its focus,

20 cm

beyond

L_{1}

. This image lies

60 - 20 = 40 cm

in front of the second lens and acts as its object, so

u = - 40 cm

with

f = + 20 cm

. The lens equation

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

gives

\frac{1}{v} = \frac{1}{20} - \frac{1}{40} = \frac{1}{40}

, so

v = 40 cm

beyond

L_{2}

. Measured from the first lens, the final image is at

60 + 40 = 100 cm

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Integer answer

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