Question

two identical coherent sources produces a zero order bright fringe on a screen if beta is the bandwidth the minimum distance between the two points on either side of a bright fringe where the intensity is of the top maximum intensity is​

Answer 1

Answer:

The answer will be beta/4

Explanation:

According to the problem the bandwidth of the fringe is beta

Now it is given that the two points are situated as the intensity is half

Now let the distance between the two points is x

Now we know that Intensity(p) = I0 x cos^θ /2

                               => I0/2 = I0 x cos^θ /2

                             θ= pie/2

Phase difference = θ = pie/2 = 2 pie /λ x Δ x

                                  path difference  => Δ x = λ /4

Therefore ,

Δ x = n λ

=> λ/4 = n λ

=> n = 1/4

the distance between central maxima to nth position is s=  n λ D/d

Now we know λ D/d = beta

Therefore s = beta /4