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  • In a double-slit experiment, at a certain point on the screen the path difference betweeen the two interfering waves is th of a wavelength. The ratio of the

In a double-slit experiment, at a certain point on the screen the path difference betweeen the two interfering waves is \frac{1}{8}th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :
Option: 1 0.568
Option: 2 0.853
Option: 3 0.760
Option: 4 0.672

 

Answers (1)

best_answer

 

 

   

 

Intensity is given by I=I_{0} \cos ^{2}\left(\frac{\Delta \phi}{2}\right)

 

Where IO=maximum intensity=intensity of light at the center of a bright fringe

 

and  using the Relation   \Delta x=\frac{2\pi }{\lambda }\Delta \phi

 

we get \frac{I}{\mathrm{I}_{0}}=\cos ^{2}\left[\frac{\frac{2 \pi}{\lambda} \times \Delta x}{2}\right]=\cos ^{2}\left(\frac{\pi}{8}\right) ; \quad \frac{I}{\mathrm{I}_{0}}=0.853

 

Hence the correct option is (2).

Posted by

vishal kumar

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