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Let S(1) and S(2) be the two slits in Yo...

Let `S_(1)` and `S_(2)` be the two slits in Young's double-slit experiment. If central maxima is observed at P and angle `/_ S_(1) P S_(2) = theta`, then fringe width for the light of wavelength `lambda` will be (assume `theta` to be a small angle)

A

`lambda // theta`

B

`lambda theta`

C

`2 lambda // theta`

D

`lambda // 2 theta`

Text Solution

Verified by Experts

The correct Answer is:
a

In `Delta S_(1) P O`,
`tan.(theta)/(2) = (d // 2)/(D)`
As `D gt gt d, theta` is very small.
`:. tan ((theta)/(2)) = (theta)/(2) implies (theta)/(2) = (d)/(2D) implies (D)/(d) = (1)/(theta)`
`:.` Fringewidth `= (lambda D)/(d) = (lambda)/(theta)`.
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