Explanation:

The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-

quarter of the distance between two fringes from the centre is

(A) 2

(B) 1/2

(C) 4

(D) 16

We have the formula for the intensity at a point in the interference pattern,

I=4I0cos2(ϕ/2) … … … … (1)

I0 is the intensity due to either of the slit and ϕ is the phase difference between the waves emitted from the two slits.

At the centre of the bright fringe the two waves are in phase (ϕ=0) and hence the intensity,

I1=4I0

Since the phase difference between the successive fringes is 2π hence the phase difference between the centre of a bright fringe and at a point one quarter of the distance between the two fringes away is 2π/4=π/2. This then from equation (1) gives the intensity I2 at that point,

I2=4I0cos2(π/4)=2I0

And, I1/I2=2