Compare the intensities of two points located at respective distance `(beta)/(4)` and `(beta)/(3)` from the central maxima in a interference of YDSE (`beta` is the fringe width)

Explanation

`Delta theta = (2 pi)/(lambda) Delta x = (2pi)/(lambda)((d)/(D)(beta)/(4)) = (2pi)/(lambda)((dD)/9) ((lambda D)/(4 d))`
`:. Delta theta = (2 pi)/(4) = (pi)/(2) rArr I = 4 I_(0) cos^(2) ((pi)/(4))`
Similarly
`Delta theta = (2pi)/(3) rArr I = 4 I_(0) cos^(2) ((2pi)/(2 xx 3))= I_(0)`
`:. ` required ratio = 2 : 1