Question

The centre of an interference pattern is always observed bright because the path difference at the centre is ....
(A) π
(B) π/2
(3) 0
(4) 3π/2​

Answer 1

Answer:

A is a correction ppllel

Answer 2

Answer:

answer is (3) 0

Explanation:

simple answer is because interference in most of the experiments like Young's Double Slit (YDSE) or even Fresnel biprism expt. we observe a central bright spot, because the light from two point sources are symmetric and have a zero path difference ( path difference is usually written in terms of lambda, and phase difference is usually written in terms of Pi, one lambda = 2 pi ).  So we have a bright spot at the center.

But you have to note that this case is not always true, in case of interference patterns, on Newton's Rings at the center we have a dark spot, because the the light undergoes a path difference of lambda/2 ( phase diff. of pi ) because bouncing off a denser medium and coming back to the eye piece.

Even in the case of a double slit experiment, if we place a mica sheet ( any material with a refractive index "n" ) if causes the fringes to shift, in other words the central fringe may not by bright anymore.

If you really want to generalize then,

you would have to see at any point where interference is occurring, if we have a phase difference of  :

0, 2pi , ..2npi (where n = 0,1,2...)  then it is a bright fringe ( or spot)

pi, 3pi , ..(2n-1)pi (where n = 1,2...)  then it is a dark fringe ( or spot)

P.S. - In practical terms we look for a central bright, because we reserve that position for central maxima for reference. ( we might manipulate the layout to serve our purpose, but like Newton's rings above sometimes we might not be able to get a central bright. )