Question

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 1

The correct option is C 1.2

Thickness of glass plate $\left(t\right)=6cm$;
Distance of the object $\left(u\right)=8cm$
And distance of the image $\left(v\right)=12cm$
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, $x+8=12+6-x\Rightarrow x=5cm$
Therefore, refractive index of glass $=\frac{Realdepth}{Apparentdepth}=\frac{6}{5}=1.2$

Why this question? Concept: The distance of image from the apparent position of plane mirror is same as the distance of object from the apparent position of plane mirror.