A plano convex lens of refractive index 1.5 and radius of curvature… | JEE Main 2004 (AIEEE)

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Combination of Lenses

A plano convex lens of refractive index $1.5$ and radius of curvature $30\text{ cm}$ 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 an object be placed in order to have a real image of size of the object

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Answer: (c)

Lens: $f_L = \frac{R}{\mu-1} = \frac{30}{0.5} = 60\text{ cm}$ ; silvered curved surface: concave mirror $f_m = 15\text{ cm}$ .
$\frac{1}{F} = \frac{2}{f_L} + \frac{1}{f_m} = \frac{2}{60} + \frac{1}{15} = \frac{1}{10} \Rightarrow F = 10\text{ cm}$
Real image of the same size forms when the object is at $2F = 20\text{ cm}$ .
So the answer is (c) 20 cm.

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Combination of Lenses question from JEE Main 2004 (AIEEE)

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