35. The radius of curvature of a thin plano convex lens is 10 cm (of curved surface) and the refractive index is 1.5 . If the plane surface is silvered, then it behaves like a concave mirror of focal length ?

35. The radius of curvature of a thin plano convex lens is 10 cm (of curved surface) and the refractive index is 1.5 . If the plane surface is silvered, then it behaves like a concave mirror of focal length ?

(a) 10 cm

(b) 15 cm

(c) 20 cm

(d) 5 cm

Answer :  (a) 10 cm

\(R = \infty\)

\(f = \infty\)

\(R = 2f\)

\(\frac{1}{f} = \frac{1}{f_{\text{lens}}} + \frac{1}{f_{\text{mirror}}} + \frac{1}{f_{\text{lens}}}\)

\(\frac{1}{f_{\text{lims}}} = \frac{2}{f_{\text{lens}}}\)

\(\frac{1}{f_{\text{combo}}} = \frac{2}{20}\)

\(f_{\text{combo}} = 10 \ \text{cm}\)

\(\frac{1}{f_{\text{lens}}} = (n_{21} - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\)

\(= (1.5 - 1) \left( \frac{1}{10} - \frac{1}{\infty} \right)\)

\(= \frac{1}{2} \left( \frac{1}{10} \right)\)

\(f_{\text{lens}} = 20 \ \text{cm}\)