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In the set up shown in figure dltltD and...

In the set up shown in figure dltltD and d=4lambda, find.

(a) total number of maximas and minimas on the screen
(b) y-coordinates corresponding to minima nearest to O.

Text Solution

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(a) In the given set up, dltltD , therefore we can use
`Deltax = d cos theta`
`(Deltax)_min = 0 `at `theta = 90^@`
` (Deltax)_max = d = 4 lambda` at `theta = 0^@`
Therefore, total number of maximas are eight corresponding to
`Deltax = +- 4lambda,+-3lambda, +-2lambda and +-lambda`
(b) Minima nearest to O are corresponding to
`Deltax = +-3.5 lambda`
`:. d cos theta = +- 3.5lambda or 4lambda cos theta = +-3.5lambda`
or ` theta = +- cos^(-1)(3.5lambda/4lambda)` or `theta = +- cos^(-1)(7/8)`
Now, `y/D = tan theta rArr y= D tan theta`
`:. y= +- D tan { cos^-1 (7/8)} ` .
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