Question

One face of a rectangular glass plate of thickness 6 cm is silvered. an object is placed at a distance of 8 cm in front of the unsilvered face. Its image is formed 10 cm behind the silvered face. The refractive index of glass plate is :

• A. $\frac{5}{3}$
• B. $\frac{4}{3}$
• C. $\frac{7}{6}$
• D. $\frac{3}{2}$

Answer 1

The correct option is D $\frac{3}{2}$

Let the refractive index of medium be $\eta$. The thickness of glass slab is $6xcm$. But due to refraction, the appeared thickness would be different ($<6xcm$) as $\eta >1$.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be $(8+x)xcm$.

Also the appeared distance of the image from silvered surface would be $(6-x+10)xcm=(16-x)xcm$.

By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.
Thus, $8+x=16-x$.

Solving the equation above, we get, $x=4xcm$.

As, $\eta =\frac{\text{Distance in vacuum air}}{\text{Distance in material}}=\frac{6}{4}=1.5$

So the refractive index of the glass is equal to $1.5$