Question

Q30. Vrite essential condition to get
sustained interference. Find out an
expression for position of maxima and
mi ma in Young's double slit experiment ​

Answer 1

Answer:

Interference of light: When two waves of same frequency and constant initial phase difference travel in the same direction along a straight line simultaneously. they superpose in such a way that the intensity of the resultant wave is maximum at certain points and minimum at certain other points. This phenomenon of redistribution of energy due to superposition of two waves of same frequency and constant initial phase difference is called interference.

Conditions for Sustained Interference of Light Waves

To obtain sustained (well-defined and observable) interference pattern, the intensity must be maximum and zero at points corresponding to constructive and destructive interference. For the purpose following conditions must be fulfilled:

i. The two interfering sources must be coherent and of same frequency. i.e.. the sources should emit light of the same wavelength or frequency and their initial phase should remain constant. If this condition is not satisfied the phase difference between the interfering waves will vary continuously. As a result the resultant intensity at any point will vary with time being alternately maximum and minimum. just like the phenomenon of beats in sound.

ii. The interfering waves must have equal amplitudes. Otherwise the minimum intensity will not be zero and there will be general illumination.

The variation of intensity I versus the position x on the screen in Young's experiment.

Fringe width, β=

d

Dλ

.

(i) β∝D, therefore with the decrease of separation between the plane of slits and screen, the fringe width decreases.

(ii) On increasing the separation between two slits (d), the fringe separation decreases as β is inversely proportional to d (i.e. β∝

d

1

.)