A point object is placed at a distance of 20 | vedclass

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(C) The system consists of a lens and a mirror. When the plane surface is silvered,the effective focal length $F$ of the system is given by $\frac{1}{

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$12 \ cm$ to the left of $AB$

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(C) The system consists of a lens and a mirror. When the plane surface is silvered,the effective focal length $F$ of the system is given by $\frac{1}{F} = \frac{2}{f_l} + \frac{1}{f_m}$.Here,the focal length of the lens $f_l = 15 \ cm$ and the focal length of the plane mirror $f_m = \infty$.So,$\frac{1}{F} = \frac{2}{15} + \frac{1}{\infty} = \frac{2}{15}$.The system acts as a concave mirror with focal length $F = 7.5 \ cm$.Using the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f_{eff}}$,where $f_{eff} = -F = -7.5 \ cm$ (since it acts as a concave mirror) and $u = -20 \ cm$:$\frac{1}{v} + \frac{1}{-20} = \frac{1}{-7.5} \Rightarrow \frac{1}{v} = \frac{1}{-7.5} + \frac{1}{20} = \frac{-20 + 7.5}{150} = \frac{-12.5}{150} = -\frac{1}{12}$.Thus,$v = -12 \ cm$.The negative sign indicates that the image is formed $12 \ cm$ to the left of the lens surface $AB$.

$A$ point object is placed at a distance of $20 \ cm$ from a thin plano-convex lens of focal length $15 \ cm$. If the plane surface is silvered,then the image formed is:

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