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Wave Optics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsWave Optics5 Marks
Question
What is interference of light? Write two essential conditions for sustained interference pattern to be produced on the screen.
Draw a graph showing the variation of intensity versus the position on the screen in Young’s experiment when (a) both the slits are opened and (b) one of the slits is closed.
What is the effect on the interference pattern in Young’s double slit experiment when:
  1. Screen is moved closer to the plane of slits?
  2. Separation between two slits is increased?
Explain your answer in each case.
✓

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:

  1. 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.
  2. 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, $\beta=\frac{\text{D}\lambda}{\text{d}}.$

  1. $\text{B}\alpha\text{D},$ therefore with the decrease of separation between the plane of slits and screen, the fringe width decreases.
  2. On increasing the separation between two slits (d), the fringe separation decreases as β is inversely proportional to d $(\text{i.e.,}\beta\alpha\frac{1}{\text{d}}.)$

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