1.

Two identical beam A and B of plane coherent waves of the sasme intensity and wavelength lambda fall on a plane screen. The direction of thebeam propagations make angles theta_(1) and theta_(2) with the normal to the screen and lie in the same plane as shown in the figure. Find the distance beta between adject interfrence fringes on the screen.

Answer»

`(lambda)/(sin theta-sin theta_(2))`
`(lambda)/(sin theta_(1)+sin theta_(2))`
`(lambda(sin theta_(1)-sin theta_(2)))/(sin theta_(1)+sin theta_(2))`
`(lambda(sin theta_(1)+sin theta_(2)))/(sin theta_(1)-sin theta_(2))`

Solution :Let P be the central BRIGHT fringe

Path difference between A 'P' and B'P' is
`DELTA X =y sin theta_(1) - y sin theta_(2)`
`Delta x = y(sin theta_(1) - sin theta_(2))`
For bright fringes `Delta x =N lambda`
`n lambda = y (sin theta_(1) - sin theta_(2))`
`y = (n lambda)/(sin theta_(1) - sin theta_(2))`
`:. beta = (lambda)/(sin theta_(1)-sin theta_(2))`


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