An object is placed at a distance of 30,cm fr | vedclass

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

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$20$

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(A) For the convex lens,the object distance $u = -30\,cm$ and focal length $f = +20\,cm$.Using the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$:$\frac{1}{v} - \frac{1}{-30} = \frac{1}{20}$$\frac{1}{v} = \frac{1}{20} - \frac{1}{30} = \frac{3-2}{60} = \frac{1}{60}$So,$v = +60\,cm$. The image formed by the lens is at $60\,cm$ from the lens.The distance between the lens and the mirror is $20\,cm$. Thus,the image formed by the lens is at a distance of $60 - 20 = 40\,cm$ behind the mirror.For the image to coincide with the object,the rays must strike the mirror normally,meaning they must be directed towards the center of curvature of the mirror.Therefore,the distance from the mirror to the image point must be equal to the radius of curvature $R$ of the mirror.$R = 40\,cm$.The focal length of the mirror is $f_m = \frac{R}{2} = \frac{40}{2} = 20\,cm$.

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