JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Geometrical Optics

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A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is ______ mm.

Answer: 280

Solution

In a two-lens collimated beam expander the lenses share a common focal point, so the angular magnification equals the ratio of focal lengths, which in turn equals the ratio of the output and input beam diameters:

\frac{f _{2}}{f _{1}} = \frac{d _{2}}{d _{1}}

. Hence

f_{2} = f_{1} \frac{d _{2}}{d _{1}} = 40 \times \frac{14}{2} = 280 mm

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Integer answer

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