In a interference arrangement similar to Young's double-slit experiment ,the slits `S_(1)` and `S_(2)` are illuminated with coheremt microwave source ,each of frequencies `10^(6)` Hz.The source are syhronized to have zero phase difference.The slits are separated by a distance from `S_(1)` and `S_(2)` where theta is defined as shown if `I_(0)` is the maximum intensity then

Options

A. `I(theta)=(I_(0))/(2)` for `theta=30^(@)`
B. `I(theta)=(I_(0))/(4)` for `theta=90^(@)`
C. `I(theta)=(I_(0))` for `theta=90^(@)`
D. `I(theta)` is constant for all value of `theta`

Answer

A,C

Explanation

`C=nlambda rArr=(C )/(n) rArr lambda=(3xx10^(8))/(10^(6))`
`lambda=300m`
`lambda=2d rArr d=(lambda)/(2)`
path difference =`d sintheta`
(A)For `theta=30^(@)`,path difference=`dsintheta 30^(@)`
Path difference =`(lambda)/(2)xx(1)/(2)=(1)/(4)`
Phase difference a `(phi)=(pi)/(2)`
`I_(R)=I_(1)+I_(1)+2sqrt(I_(1)I_(2))cosphi`
`I_(R)=2I=(I_(0))/(2) "for" theta=0`
(c ) for `theta=0,phi=0I(theta)=I_(0)`