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  • A convex lens of focal length is placed in front of a convex mirror with principal axis coinciding each other. The distan

A convex lens of focal length 20 \mathrm{~cm} is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 \mathrm{~cm}. A point object is placed on principal axis at a distance of 60 \mathrm{~cm} from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ______________ \mathrm{cm}.

Option: 1

10


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Let the focal length of convex nirror be \mathrm{f_{0}}
If the object and image coincides then the normal incidence must occur on the mirror
For convex lens,

\mathrm{u =-60 \mathrm{~cm} }

\mathrm{v =10+2 f_0 }

\mathrm{\frac{1}{v}-\frac{1}{u} =\frac{1}{f} }

\mathrm{\frac{1}{\left(10+2 f_0\right)} -\frac{1}{(-60)}=\frac{1}{+20} }

\mathrm{\frac{1}{\left(10+2 f_0\right)} =\frac{1}{20}-\frac{1}{60}=\frac{40}{1200} }

\mathrm{2 f_0 =20 \mathrm{~cm} }
\mathrm{f_0 =10 \mathrm{~cm}}
The focal length of the convex mirror is \mathrm{10 \mathrm{~cm}}.

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Sayak

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