Given is a thin convex lens of glass (refract | vedclass

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(D) For a lens with one side silvered,the equivalent power of the system is given by $P_{eq} = 2P_{\ell} + P_{m}$.Here,$P_{\ell} = \frac{(\mu - 1)}{R}

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$R / (2\mu - 1)$

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(D) For a lens with one side silvered,the equivalent power of the system is given by $P_{eq} = 2P_{\ell} + P_{m}$.Here,$P_{\ell} = \frac{(\mu - 1)}{R}$ is the power of one surface of the lens. Since it is a convex lens,both surfaces contribute to the power.$P_{m} = -\frac{1}{f_{m}} = -\frac{1}{(-R/2)} = \frac{2}{R}$ (as the mirror formed by the silvered surface has radius $R/2$).$P_{eq} = 2 \left[ \frac{(\mu - 1)}{R} + \frac{(\mu - 1)}{R} ight] + \frac{2}{R} = \frac{4\mu - 4 + 2}{R} = \frac{4\mu - 2}{R}$.The system acts as a concave mirror with focal length $F = -\frac{1}{P_{eq}} = -\frac{R}{4\mu - 2} = -\frac{R}{2(2\mu - 1)}$.For the image to form on the object itself,the object must be placed at the center of curvature of this equivalent mirror.The distance is $d = 2|F| = 2 	imes \frac{R}{2(2\mu - 1)} = \frac{R}{2\mu - 1}$.

Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature $R$. One side is polished for complete reflection. At what distance from the lens,an object be placed on the optic axis so that the image gets formed on the object itself?

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