The flat face of a plano-convex lens of focal | vedclass

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(B) When a lens is silvered,it acts like a mirror with an equivalent focal length $f_{eq}$.The formula for the equivalent focal length is given by $\f

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real image $6 \,cm$ away from the lens

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(B) When a lens is silvered,it acts like a mirror with an equivalent focal length $f_{eq}$.The formula for the equivalent focal length is given by $\frac{1}{f_{eq}} = \frac{2}{f_l} + \frac{1}{f_m}$,where $f_l$ is the focal length of the lens and $f_m$ is the focal length of the mirror.For a plano-convex lens,$f_l = 10 \,cm$. The flat surface is silvered,so it acts as a plane mirror,meaning $f_m = \infty$.Thus,$\frac{1}{f_{eq}} = \frac{2}{10} + \frac{1}{\infty} = \frac{1}{5}$.Since the system acts as a concave mirror,we take $f_{eq} = -5 \,cm$ (using sign convention for a mirror).Given the object distance $u = -30 \,cm$,we use the mirror formula: $\frac{1}{f_{eq}} = \frac{1}{v} + \frac{1}{u}$.Substituting the values: $\frac{1}{-5} = \frac{1}{v} + \frac{1}{-30}$.$\frac{1}{v} = \frac{1}{-5} + \frac{1}{30} = \frac{-6 + 1}{30} = \frac{-5}{30} = -\frac{1}{6}$.Therefore,$v = -6 \,cm$.The negative sign indicates that the image is formed in front of the mirror,which means it is a real image at a distance of $6 \,cm$ from the lens.

The flat face of a plano-convex lens of focal length $10 \,cm$ is silvered. $A$ point source placed $30 \,cm$ in front of the curved surface will produce a

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