In YDSE of equal width slits, if intensity at the center of screen is `I_(0)`, then intensity at a distance of `beta // 4` from the central maxima is

Options

A. `I_(0)`
B. `(I_(0))/(2)`
C. `(I_(0))/(4)`
D. `(I_(0))/(3)`

Answer

b

Explanation

Let the intensity of individual waves be. I Then
`I_(0) = 4 I implies I = (I_(0))/(4)`
At P,
`Delta x = d sin theta`
`implies Delta x d sin theta = (d y)/(D)`
`implies Delta x = (d)/(D) xx (beta)/(4) = (d)/(D) xx (lambda D)/(4 d) = (lambda)/(4)`
`:. Delta phi = (2 pi)/(lambda) xx (pi)/(4) = (pi)/(2)` `[Delta phi = k Delta x]`
`I' = I + I + 2 sqrt(I^(2)) cos ((pi)/(2)) = 2 I = (I_(0))/(2)`