A point source of light is kept at a distance of 150 cm from a converging lens, on its optical axis. The focal length of the lens is 100 cm and its diameter is 3 cm. A screen is placed on the other side of the lens, perpendicular to the axis of lens, at a distance 200 cm from it. Then find the area of the illuminated part of the screen? (Assume all rays incident on lens as paraxial)
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Question

A point source of light is kept at a distance of 150 cm from a converging lens, on its optical axis. The focal length of the lens is 100 cm and its diameter is 3 cm. A screen is placed on the other side of the lens, perpendicular to the axis of lens, at a distance 200 cm from it. Then find the area of the illuminated part of the screen? (Assume all rays incident on lens as paraxial)

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: Use the thin-lens formula 1/f = 1/v - 1/u with m = v/u. For lens material/medium changes use the lens-maker relation with the relative refractive index; powers of thin lenses in contact add. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is π/4 cm². Therefore the correct option is A.