In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in fron

Question

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is\

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(a) : For lens, $u=-20 \mathrm{~cm}, f_{l}=15 \mathrm{~cm}, v=$ ? $$ \begin{aligned} \frac{1}{v}-\frac{1}{u}=\frac{1}{f_{l}} \Rightarrow \frac{1}{v}-\frac{1}{-20}=\frac{1}{15} \ \Rightarrow \frac{1}{v}=\frac{1}{15}-\frac{1}{20}=\frac{1}{60} 	herefore v=60 \mathrm{~cm} \end{aligned} $$ To obtain its real image on object's place.\ The center of curvature of the convex mirror must be at the position of virtual image, i.e., at 60 cm\ According to given figure, $5+2 f_{R}=60$\ $\Rightarrow 2 f_{R}=55 \Rightarrow f_{R}=27.5 \mathrm{~cm}$\