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A bichromatic light having wavelength ga...

A bichromatic light having wavelength `gamma_1` and `gamma_2` falls normally on a single slit and produces a diffraction pattern. It is found that the first diffraction minimum for `gamma_1` is at `30^(@)` and second diffraction minimum for `gamma_2` is at `45^(@)` from the central maximum. If `gamma_1` is `5000xx10^(-8)` cm, then the value of `gamma_2` is close to:

A

`3536 xx 10^(-8) cm`

B

`7071 xx 10^(-8) cm`

C

`2887 xx 10^(-8) cm`

D

`3660 xx 10^(-8) cm`

Text Solution

Verified by Experts

The correct Answer is:
A
`d sin 30^@ = lambda_1 , d sin 45^@= 2 lambda_2`
`implies (lambda_1)/(2 lambda_2) = 1/(sqrt2) implies lambda_2 = (lambda_1)/(sqrt(2)) = 3536 xx 10^(-8) cm`
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