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  • A luminous object is placed at a distance of from a convex lens of focal length

A luminous object is placed at a distance of \mathrm{30\ cm} from a convex lens of focal length \mathrm{20\ cm}. On the other side of the lens, at what distance from the lens must a convex mirror of radius of curvature \mathrm{10\ cm} be placed in order to have an upright image of the object coincident with it?

Option: 1

\mathrm{12\ cm}


Option: 2

\mathrm{30\ cm}


Option: 3

\mathrm{50\ cm}


Option: 4

\mathrm{60\ cm}


Answers (1)

best_answer

This is possible when the rays are incident on the mirror normally, i.e., the image by the lens is formed at the centre of curvature of the mirror.
\mathrm{\text { Now, }\ \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}} \quad \text { or } \quad \frac{1}{20}=\frac{1}{\mathrm{v}}+\frac{1}{30}}
\mathrm{\therefore \quad \frac{1}{\mathrm{v}}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60} \text { or } \quad \mathrm{v}=60 \mathrm{~cm}}

From figure, the distance of mirror from lens is,
\mathrm{\mathrm{LM}=\mathrm{LC}-\mathrm{MC}=60-10=50 \mathrm{~cm}}

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Pankaj

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