Question

Bichromatic light is used in YDSE having wavelengths ${\lambda }_1=400nm$ and ${\lambda }_2=700nm$. Find the minimum order of ${\lambda }_1$ which overlaps with ${\lambda }_2$.

Answer 1

Let $m^{th}$ bright fringe of first light overlaps with $n^{th}$ bright fringe of second light.

$\therefore \frac{m\times 400nm\times D}{d}=\frac{n\times 700nm\times D}{d}\Rightarrow \frac{m}{n}=\frac{7}{4}$

$\Rightarrow 7^{th}$ bright fringe of first light overlaps with $4^{th}$ bright fringe of second light (minimum).