Question

A beam of light is converging towards a point on the screen. If a plane parallel plate of glass of refractive in μ and thickness t is introduced in the path of the beam, the convergent point is shifted:

A. $t\left( {1 - \dfrac{1}{\mu }} \right)$ away

B. $t\left( {1 + \dfrac{1}{\mu }} \right)$ nearer

C. $t\left( {1 + \dfrac{1}{\mu }} \right)$ away

D. $t\left( {1 - \dfrac{1}{\mu }} \right)$ nearer

Answer 1

Velocity of light will be different in different media. If velocity of light is higher in one medium and lesser in another medium then the first one is called a rarer medium and the second one is called denser medium. The path travelled by light also varies with its velocity.

Formula used:
Apparent depth = $\dfrac{t}{\mu }$

Complete answer:
Velocity is nothing but the rate of change of displacement i.e the ratio of displacement to the time taken. So the time taken will be displacement upon the velocity.
Velocity of light in any medium of refractive index(n) will be
$v = \dfrac{c}{n}$ where ‘c’ is the velocity of light in the free space and ‘n’ is the refractive index of the medium.
For example let us consider the case of air and water and then we apply the same to the slab given here.
For air, the refractive index will be one. The water refractive index will be greater than one. Hence when light enters from water to air, its velocity increases. In order to maintain the same time displacement also must increase. That means the path travelled in the air by the light must increase. This will be possible if the light bends away from the normal. This is clearly shown in the diagram below.

So actually if the object is at ‘d’ depth in the water, due to the change in medium the image will appear nearer i.e distance ‘d’ would be reduced to $\dfrac{d}{\mu }$.
So the shift will be $d - \dfrac{d}{\mu }$ along the direction of light travel.
So similarly if we compare the slab with water, the shift will be
Real depth – apparent depth
Real depth = t
Apparent depth = $\dfrac{t}{\mu }$
So shift is $t - \dfrac{t}{\mu }$ along the direction of light, i.e away from the previous point on the screen.

Hence option A is correct answer.

Note:
This phenomenon helps aquatic animals a lot. The fish which is at a certain position in water appears very nearer to the pelican which tries to hunt the fish. So when a pelican tries to catch the image of fish, that fish will become alert and dive into water to save itself from the pelican.