12. One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face forms an image 12 cm behind the silvered face. The refractive index of the glass is ?

12. One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face forms an image 12 cm behind the silvered face. The refractive index of the glass is ?

(a) 0.4

(b) 0.8

(c) 1.2

(d) 1.6

Answer :  (c) 1.2

\( AD = \frac{RD}{\mu} \)

Apparent shift \( (AS) = RD - AD \)

\( = RD - \frac{RD}{\mu} \)

\( = RD \left(1 - \frac{1}{\mu} \right) \)

Object distance = Image distance

\( 8\,\text{cm} + AD = 12\,\text{cm} + AS \)

\( 8 + \frac{6}{\mu} = 12 + 6\left(1 - \frac{1}{\mu} \right) \)

\( \frac{12}{\mu} = 4.8 \)

\( \mu = \frac{12}{10} = 1.2 \)