A plano-convex lens behaves as a concave mirror of focal length 30 cm when its plane surface is silvered and as a concave mirror of focal length 10 cm when its curved surface is silvered. What is the radius of curvature of curved surface and `mu` of the material of lens?

Explanation

To solve the problem, we need to analyze the behavior of the plano-convex lens when its surfaces are silvered and how it behaves as a concave mirror in both cases.

### Step 1: Understanding the first case (Plane surface silvered)
When the plane surface of the plano-convex lens is silvered, it behaves like a concave mirror with a focal length (F1) of 30 cm. For a concave mirror, the focal length is given by:

\[ \frac{1}{F} = \frac{2}{f_1} + \frac{1}{f_m} \]
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