The ratio of the intensity at the cnetre of a bright fringe to the intensity at a point one quarter of the fringe width from the centre is

Options

A. 2
B. `1/2`
C. 4
D. 16

Answer

A

Explanation

Two waves of a single source having an amplitude A interfere. The resulting amplitude
`A_(r)^(2)=A_(1)^(2)+A_(2)^(2)+2A(1)A cosdelta`
where `A_(1)`=` A_(2)` = A and `delta` = phase difference between the waves
`implies_(1)+l_(2) +2sqrt (l_(1),l_(2)) cosdelta` When the maxima occurs at the center, `delta` = 0`impliesl_(r2)=41`
Since the phase difference, between two successive fringes is 2n, the phase difference between two points separated by a distance equal to one quarter of the distance between the two, successive fringes is equal to `delta = (2pi) (1/4) = pi/2` radian
`l_(r2)=4l cos^(2)[(pi//2)/2]=2l`.....(2)
Using(1)and(2)
`l_(r1)/l_(r2)=41/21=2`
Hence (A) is correct.