Question

White light is used in a Young's double slit experiment. Find the minimum non zero order of the violet fringe$(\lambda =400nm)$ which overlaps with a red fringe $(\lambda =700nm)$ .

Answer 1

Let $m^{th}$ bright fringe of violet light overlaps with $n^{th}$ bright fringe of red 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 violet light overlaps with $4^{th}$ bright fringe of red light (minimum ). Also, it can be seen that ${14}^{th}$ violet fringe will overlap $8^{th}$ red fringe.
Because, $m/n=7/4=14/8$.