A convex lens of focal length 15,cm is placed | vedclass

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(D) For the image to coincide with the object,the light rays must strike the mirror normally (perpendicularly) so that they retrace their path back th

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$55$

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(D) For the image to coincide with the object,the light rays must strike the mirror normally (perpendicularly) so that they retrace their path back through the lens to the object position.This means the rays emerging from the lens must be directed towards the center of curvature $(C)$ of the convex mirror.Let the distance between the lens and the mirror be $d = 5\,cm$.Let the object distance from the lens be $u = -20\,cm$ and the focal length of the lens be $f = 15\,cm$.Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$:$\frac{1}{15} = \frac{1}{v} - \frac{1}{-20}$$\frac{1}{v} = \frac{1}{15} - \frac{1}{20} = \frac{4-3}{60} = \frac{1}{60}$So,$v = 60\,cm$.The image formed by the lens acts as an object for the mirror. Since the rays must strike the mirror normally,the image formed by the lens must be at the center of curvature of the mirror.The distance of the center of curvature from the lens is $v = 60\,cm$.The distance of the mirror from the lens is $5\,cm$.Therefore,the radius of curvature $R$ of the mirror is the distance from the mirror to its center of curvature:$R = v - d = 60\,cm - 5\,cm = 55\,cm$.

$A$ convex lens of focal length $15\,cm$ is placed in front of a convex mirror. When an object is placed at $O$,the image coincides with it. The radius of curvature of the mirror is.....$cm$.

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