Question 229 of 295

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

A$20.0cm$B$30.5cm$C$25.0cm$D$27.5cm$

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Answer: (D) $27.5cm$

Image by Lens -

$-\dfrac{1}{-20}+\dfrac{1}{v}=\dfrac{1}{+15}$

$V=+60$

Distance of Image from mirror $=60-5=55cm$

Path retraces when that image in at center of curvature of the mirror. Hence

$R=55cm$

${f}_{mirror}=\dfrac{R}{2}=27.5cm$