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Wave Optics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsWave Optics3 Marks
Question
  1. Why are coherent sources necessary to produce a sustained interference pattern?
  2. In Young's double slit experiment using monochromatic light of wavelength$\lambda,$ the intensity of light at a point on the screen where path difference is$\lambda,$ is K units. Find out the intensity of light at a point where path difference is $\lambda/3.$
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Answer

  1. Coherent sources are needed to ensure that the positions of maxima and minima do not change with time.
Alternate Answer

Coherent sources have constant phase difference and, therefore, produce a sustained interference pattern.
  1. $\text{I} = \text{I}_{1} + \text{I}_{2} + 2 \sqrt{\text{I}_{1}\text{I}_{2}}\cos\theta$
For path difference $\lambda,$ phase difference

$\Phi = 2\pi$

$\text{Hence}, \text{k} = 4\text{I}_{0}\cos^{2}\pi =4 \text{ I}_{0}$

For path difference $\lambda\big/3$

Phase difference $\Phi = 2\pi\big/3$

Intensity

$\text{I}' = 4\text{I}_{0}\cos^{2}\pi\big/3$

$ = 4\text{I}_{0}\bigg(\frac{1}{2}\bigg)^{2} = \text{I}_{0}$

Therefore, $\text{I}' = \frac{\text{k}}{4}.$

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