A travelling microscope is focused on an ink dot. When a glass slab (n=1.5) of thickness $\ 9cm$ is introduced on the dot, the travelling microscope has to be moved by:
$A.\ 3cm\ upwards$
$B.\ 9cm\ upwards$
$C.\ 3cm\ downwards$
$D.\ 9cm\ downwards$

Hint: On placing the glass slab in between, there will be a shift in position of image. The distance by which the microscope has to be shifted in order to focus again, is the same as the shift observed in the image on inserting the slab. Hence if somehow we’re able to find the shift in the image on inserting a glass slab, we’re done.

Formula used:
$s=t\left( 1-\dfrac { 1 }{ n } \right)$, where
s = shift in the image
t = thickness of the slab
n = refractive index of the slab

Complete step-by-step answer:
Given:–
t = 9cm
n = 1.5
Now, putting values in the formula
 $s=9\left( 1-\dfrac { 1 }{ 1.5 } \right)$
$s =9\left( 1-\dfrac { 2 }{ 3 } \right)$
$s = 9\left( \dfrac { 1 }{ 3 } \right) =3cm$
Hence the microscope must be lifted upwards by 3cm to again focus the dot.
Hence A. is the correct option.

Additional information:
Paraxial rays- These are the rays which are assumed close to the axis and making very small angles with the optical system. These are assumed for easier calculations.
Students might wonder about the shifting of the image. The main reason for the shift is the change of medium (basically change of refractive index of medium). Whenever a light ray observes a change of medium, it may bend towards or away from the normal, depending upon the nature of medium

Note: The shift of image as seen by the observer for paraxial rays from glass slab is independent of the distance of microscope from the glass slab and also it is independent of the placement of the dot.
Hence in both cases, the formula will remain the same,$s\quad =\quad t\left( 1-\dfrac { 1 }{ n } \right)$. Also, it can be observed from the shift formula, that shift is always less than or equal to ‘t’ (Almost equal if the medium’s refractive index is very large). Hence we can say that the image will always remain inside the glass slab. But the statement is valid when the distance of ink dot from glass slab is almost negligible. If so, then we can’t say anything unless analysed.