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The coherent point sources S(1) and S(2)...

The coherent point sources `S_(1)` and `S_(2)` vibrating in same phase emit light of wavelength `lambda`. The separation between the sources is `2lambda`. Consider a line passingh through `S_(2)` and perpendicular to the line `S_(1)S_(2)`. What is the smallest distance from `S_(2)` where a minimum of intensity occurs due to interference of waves from the two sources?

Text Solution

Verified by Experts

At` S_2, Deltax= 2lambda`
Therefore, the minima closest to `S_2` will be corresponding to the path
difference `Deltax = (3lambda)/2`. Suppose this point is P at a distance y from `S_2`.Then,
`S_1P - S_2P = (3lambda)/2`
`sqrt(y^2 + (S_1 S_2)^2) -y = (3lambda)/2`
or ` sqrt(y^2+(2lambda)^2) = (y + (3lambda)/2)`
Squaring and then solving this equation, we get
`y= (7lambda)/12`.
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Knowledge Check

  • Two coherent point sources S_1 and S_2 vibrating in phase emit light of wavelength lamda The separation between the sources is 2lamda . The smallest distance from S_2 on a line passing through S_2 and perpendicular to S_1S_2 where a minimum intensity occurs is

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  • Choose the most appropriate option. Two coherent point sources S_(1) and S_(2) vibrating in phase emit light of wavelength lambda . The separation between them is 2lambda . The light is collected ona screen placed at a distance D gt gt lambda from the slit S_(1) as shown. The minimum distance, so that intensity at P is equal to intensity at O.

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