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(C) For the convex lens,the object distance $u = -30 \,cm$ and focal length $f = +20 \,cm$. Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{

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$50$

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(C) For the convex lens,the object distance $u = -30 \,cm$ and focal length $f = +20 \,cm$. Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$:$\frac{1}{20} = \frac{1}{v} - \frac{1}{-30}$$\frac{1}{v} = \frac{1}{20} - \frac{1}{30} = \frac{3-2}{60} = \frac{1}{60}$So,$v = 60 \,cm$. This means the lens forms a real image at $60 \,cm$ from the lens.For the final image to coincide with the object,the light rays must fall normally on the convex mirror so that they retrace their path. This happens if the rays are directed towards the center of curvature of the mirror.The radius of curvature of the mirror is $R = 10 \,cm$. Thus,the mirror must be placed such that its center of curvature coincides with the image formed by the lens.The distance of the mirror from the lens is $d = v - R = 60 \,cm - 10 \,cm = 50 \,cm$.

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