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(C) In the absence of the convex mirror,the real and inverted image of the object is formed at a distance $v$ from the convex lens. Using the lens for

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$25$

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(C) In the absence of the convex mirror,the real and inverted image of the object is formed at a distance $v$ from the convex lens. Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$:$\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{20} + \frac{1}{-30} = \frac{3-2}{60} = \frac{1}{60}$$v = 60 \ cm$.When a convex mirror is introduced between the lens and the image position such that the final image is formed at the object $O$ itself,the light rays must strike the mirror normally. This implies that the rays are directed towards the centre of curvature of the mirror.The distance of the centre of curvature from the mirror is $R = v - d$,where $d$ is the distance between the lens and the mirror.$R = 60 \ cm - 10 \ cm = 50 \ cm$.The focal length of the mirror is $f_m = \frac{R}{2} = \frac{50 \ cm}{2} = 25 \ cm$.

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