The plane face of a plano convex lens is silvered. If μ be the...

When an object is placed in front of such a lens,the rays first of all refracted from the convex surface, then refract from the polished plane surface and again refracts from convex surface. If $f_l and f_m$ be the focal lengths of lens (convex surface) and mirror (plane polished surface) respectively, then effective focal length $F$ is given by $$\begin{aligned} & \frac{1}{F}=\frac{1}{f_l}+\frac{1}{f_m}+\frac{1}{f_l}=\frac{2}{f_l}+\frac{1}{f_m}=\frac{2}{f_l} \quad\left(\because f_m=\frac{R}{2}=\infty\right) \\ & \frac{1}{f_l}=(\mu-1)\left(\frac{1}{R}\right) \\ & \therefore \frac{1}{F}=\frac{2(\mu-1)}{R} \text{\text{ or } } F=\frac{R}{2(\mu-1)} \text{ or } R=2 F=\frac{R}{(\mu-1)}\end{aligned}$$