Question

A postage stamp kept below a rectangular glass block of refractive index $1.5$ when viewed from vertically above it, appears to be raised by $7.0mm$. Calculate the thickness of the glass block.
(A) $1.2cm$
(B) $4.2cm$
(C) $2.1cm$
(D) $3cm$

Answer 1

Hint
Refraction of light changes depth perception. Taking the thickness of the block to be the same as the real depth of the postage stamp, calculate the thickness using a refractive index formula.
$n = \dfrac{d}{{d'}}$ where $d$ is the real depth, $d'$ is the apparent depth and $n$ is the refractive index of the medium.

Complete step by step answer
When light travels from one medium to another its direction changes. This optical phenomenon is known as the refraction of light. Now in order to determine the degree up to which light bends as it changes medium is known as the refractive index. The refractive index $n$ for a given medium is given as
$n = \dfrac{c}{v}$ where $c$is the velocity of light in vacuum and $v$ is the velocity of light in the given media.
Another property of refraction is that when an object placed in a medium is viewed from another medium, its distance appears to be different than the original distance. As given in the question above, when a postage stamp kept below a rectangular glass block is observed from above (different medium), its depth appears to have changed. This virtual depth is known as apparent depth and the original thickness here is the real depth.
Another formula to calculate refractive index is
$n = \dfrac{d}{{d'}}$ where $d$ is the real depth and $d'$ is the apparent depth.
So, let us assume that the real depth be $x$
Then we must have $d' = x - 7$
Substituting these values in the above equation we get,
$\Rightarrow n = \dfrac{x}{{x - 7}} $
$\Rightarrow 1.5 = \dfrac{x}{{x - 7}} $
$\Rightarrow 1.5x - 10.5 = x $
$\Rightarrow 0.5x = 10.5 $
$\Rightarrow x = 21 $
Therefore, the thickness of the glass block is $21mm = 2.1cm$
So, the correct option is (C).

Note
When light travels from rarer to denser medium, its direction changes towards the normal and when it travels from denser to rarer medium, its direction changes away from the normal. There is no change in direction when it changes medium along the normal.