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A Plano - convex lens of refractive index 1.5 and radius of curvature 30cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens and object be placed in order to have a real image of the size of the object

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10cm

30cm

60cm

20cm

answer is A.

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Detailed Solution

$\frac{1}{F} = \frac{2}{f_{g}} + \frac{1}{f_{m}}$

$\frac{1}{F} = 2 (μ_{g} - 1) \frac{1}{R} + \frac{2}{R} \Rightarrow \frac{2 μ}{R}$

$F = \frac{R}{2 μ} \Rightarrow 10 c m$

Given $ϑ = u$

$∴ \frac{1}{f} = \frac{1}{V} - \frac{1}{- u} = \frac{1}{V} + \frac{1}{u} = \frac{2}{u}$

$u = 2 f = 2 \times 10 = 20 c m$

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