A plano convex lens has actual thickness of 3.665 cm. It appears to have thickness of 435 cm when seen normally through the flat surface while it appears to have 910 cm when seen normally through the curved surface calculate refractive Index of glass lens and the radius of curvature of the curved surface

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7.89 m

6.45 m

257 cm

7.52 cm

answer is C.

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Detailed Solution

when the observer is at A he sees through the flat surface of ‘O’ is the position of the object, then as seen from A
$μ = \frac{real depth}{apparent depth} = \frac{3 .665}{435} = 1 .505 \frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R} μ_{2} = 1, μ_{1} = 1 .505, u = 3 .665 cm, v = 9 .10 cm \frac{1}{v} = \frac{1 .505}{3 .665} = \frac{1 - 1 .505}{R} \frac{1}{2 .910} - \frac{1}{2 .435} = \frac{0 .505}{R} = \frac{0 .475}{2 .435 \times 2 .91} \Rightarrow R = 7 .52 cm$