The final image of the object forms on the ob | vedclass

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(A) For the final image to form on the object itself,the light rays must strike the mirror normally (perpendicularly) after passing through the lens.T

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$30$

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(A) For the final image to form on the object itself,the light rays must strike the mirror normally (perpendicularly) after passing through the lens.This means the rays must appear to be coming from the center of curvature of the mirror.Let the object distance from the lens be $u = -60 \ cm$ and the focal length of the lens be $f_l = +30 \ cm$.Using the lens formula,$\frac{1}{v} - \frac{1}{u} = \frac{1}{f_l}$,we get $\frac{1}{v} - \frac{1}{-60} = \frac{1}{30}$.$\frac{1}{v} = \frac{1}{30} - \frac{1}{60} = \frac{2-1}{60} = \frac{1}{60}$.So,$v = +60 \ cm$.The image formed by the lens is at a distance of $60 \ cm$ to the right of the lens.The distance between the lens and the mirror is $30 \ cm$.Therefore,the image formed by the lens is at a distance of $60 - 30 = 30 \ cm$ behind the mirror.For the rays to strike the mirror normally,this point must be the center of curvature $(C)$ of the mirror.Thus,the radius of curvature $R = 30 \ cm$.

The final image of the object forms on the object itself. If the focal length of the lens is $30 \ cm$,then the radius of curvature of the mirror is .... $cm$.

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