Question

Please Help! When does the double-slit interference have its first dark spot on either side of the central peak intensity?

A. when the paths d1 and d2 differ by one wavelength
B. when the paths d1 and d2 differ by half a wavelength
C. when the waves arrive in step, or “on phase,” with each other
D. when the paths d1 and d2 have the same length

Answer 1

A, C, and D are true when a light spot appears, so those are false.

The answer is therefore B.

Answer 2

Explanation :

In double slit experiment, the consecutive dark and bright fringes are formed in the screen.

The condition for bright fringes is :

$dsin\theta=n\lambda$

and

The condition for dark fringe is :

$dsin\theta=(n+\dfrac{1}{2})\lambda$

So, the first dark spot on either side of the central peak intensity is observed when the when the paths d₁ and d₂ differ by half a wavelength.  

Hence, the correct option is (B).