CBSE Class 12-science Answered
find the intensity at a point on a screen in young double slit experiment where the interfering wave of equal intensity have have a path difference of lemda/4,lemda/3
Asked by tannusharan31 | 05 Nov, 2023, 17:31: PM
Let
and
are the intensities of two waves that are interfering in double slit experiment.
![begin mathsize 14px style text I end text subscript 1 end style](https://images.topperlearning.com/topper/tinymce/cache/a7a5f3eb0a3f2114c7c9c613f0f27f31.png)
![begin mathsize 14px style straight I subscript 2 end style](https://images.topperlearning.com/topper/tinymce/cache/61b46244961ec247b2d3ff6814d67368.png)
Resultant Intensity
is given as
![begin mathsize 14px style straight I subscript straight R end style](https://images.topperlearning.com/topper/tinymce/cache/26a39dbaf7042e4cfe01c66ed35aec21.png)
![begin mathsize 14px style straight I subscript straight R space equals space straight I subscript 1 plus space straight I subscript 2 plus 2 square root of straight I subscript 1 space straight I subscript 2 end root space cos theta end style](https://images.topperlearning.com/topper/tinymce/cache/8c0a8a7c7cb1da54f7db215b14cd8ba8.png)
where θ is phase difference between the waves .
If path difference between waves is λ/4 , where λ is wavelength , then phase difference θ = (2π)/4 = π/2 .
If each wave has equal intensity
and path difference between waves is λ/4 , then we get resultant
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
intensity from eqn.(1) as
![begin mathsize 14px style straight I subscript straight R space equals space straight I plus space straight I plus 2 space straight I space cos left parenthesis pi divided by 2 right parenthesis space equals space 2 space straight I end style](https://images.topperlearning.com/topper/tinymce/cache/3ecf2ab6fa30788f6cce4a2f068bb910.png)
----------------------------------------------------
If path difference between waves is λ/3 , where λ is wavelength , then phase difference θ = (2π)/3.
If each wave has equal intensity
and path difference between waves is λ/3 , then we get resultant
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
intensity from eqn.(1) as
![begin mathsize 14px style straight I subscript straight R space equals space straight I plus space straight I plus 2 space straight I space cos left parenthesis 2 pi divided by 3 right parenthesis space equals space straight I space plus space straight I space minus space straight I space equals space straight I end style](https://images.topperlearning.com/topper/tinymce/cache/261dcb536fca5d62ea564aa75b2f0838.png)
Answered by Thiyagarajan K | 05 Nov, 2023, 19:50: PM
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