Question

Write the conditions on path difference under which (i) constructive and (ii) destructive interference occur in Young’s double slit experiment.

Answer 1

Condition for

(i) Constructive interference: Path difference ∆x must be an integral multiple of the wavelength of light.

i.e., $\Delta x=n\lambda ,\text{where}n=0,\pm 1,\pm 2,...$

(ii) Destructive interference: Path difference $\Delta x$ must be an odd multiple of half of the wavelength of light

i.e., $\Delta x=(2n-1)\frac{\lambda }{2}$, where $n=\pm 1,\pm 2\dots$