Question: In Young’s double slit experiment, the first maxima is observed at a fixed point P on the screen. No...

Question

In Young’s double slit experiment, the first maxima is observed at a fixed point P on the screen. Now, the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

A) Remains constant
B) Keeps on decreasing
C) First decreases and then increases
D) First decreases and then becomes constant

Answer 1

Solution

Recall that interference of light is the phenomenon in which two waves superimpose with each other in order to form a resultant wave having greater, lower or the same amplitude. In order to understand the wave theory of light, Young’s double slit experiment is used.

Complete step-By-Step solution:
Step I:
In this experiment a source of light is used and two or more slits are used for the light to be passed. The position of first maxima observed on the screen is known by using the formula
$x = \dfrac{{n\lambda D}}{d}$
Here $n = 1$
$\therefore x = \dfrac{{\lambda D}}{d}$
Where d is the separation between the slits
And D is the distance from the screen
$\lambda$ is the wavelength
Step II:
Since $x \propto D$
$\therefore$ as D increases, the maxima at point P will go upwards. But when one crest and one trough superimpose, then minima will occur and there is also a minima between O and P. The point P will have a decrease in intensity till the position of minima is reached and the intensity will increase due to central maxima.
Step III:
The ratio of intensity at point P to the intensity at point O (centre of the screen) will first decrease and then increase.

$\Rightarrow$ Option C is the right answer.

Note: It is important to note that when two waves of equal frequency and phase superimpose with each other, then they produce a single wave equal to the sum of the individual wave. The crest is the upper part of a wave and trough is the lower part of the wave. It has higher amplitude. But when the crest of one wave superimposes with the trough of another wave, then destructive interference takes place. The resultant wave has lower amplitude.