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

Thickness of glass plate (t) = 6 cm;

Distance of the object (u) = 8 cm. And distance of the image (v) = 12 cm. Let x = Apparent position of the silvered surface in cm. Since the image is formed due to reflection at the silvered face and by the property of mirror image Distance of object from the mirror = Distance of image from the mirror 

Or $x+8=12+6-x\Rightarrow x=5\mathrm{cm}$

Therefore, refractive index of glass

$=\frac{\text{ Real depth }}{\text{ Apparent depth }}=\frac{6}{5}=1.2$