When light from two sources (say slits `S_(1)` and `S_(2)`) interfere, they form alternate dark and bright fringes. Bright fringe is formed at all point where the path difference is an odd multiple of half wavelength. At the condition of equal amplitudes, `A_(1) = A_(2) = a`, the maximum intensity will be `4 a^(2)` and the visibility improves, The resultant intensity can also be indicated with phase factor as `I = 2 a^(2) cos^(2) (phi // 2)`.Using this passage, answer the following questions.
If the path difference between the slits `S_(1)` and `S_(2)` is `(lambda)/(2)` the central fringe will have an intensity of

Options

A. 0
B. `a^(2)`
C. `2 a^(2)`
D. `4 a^(2)`

Answer

a

Explanation

Path difference to the central fringe position is `lambda // 2`. Since it is an old multiple of `(lambda // 2)` the fringe formed is dark. So, choice (a) is correct and the other are wrong.