Question

White light is used in a Young's double slit experiment. Find the minimum order of the violet fringe \[\left( \lambda = 400\text{ nm} \right)\] which overlaps with a red fringe \[\left( \lambda = 700\text{ nm} \right).\]

Answer 1

Let the separation between the slits be d and distance between screen from the slits be D.

Suppose, the m^th bright fringe of violet light overlaps with the n^th bright fringe of red light.

Now, the position of the m^th bright fringe of violet light, y_v = \[\frac{m \lambda_v D}{d}\]

Position of the n^th bright fringe of red light, y_r = \[\frac{n \lambda_r D}{d}\]

For overlapping, y_{v =} y_r

So, as per the question,

\[\frac{m \times 400 \times D}{d} = \frac{n \times 700 \times D}{d}\]

\[ \Rightarrow \frac{m}{n} = \frac{7}{4}\]

Therefore, the 7^th bright fringe of violet light overlaps with the 4^th bright fringe of red light.

It can also be seen that the 14^th violet fringe will overlap with the 8^th red fringe.

Because,

\[\frac{m}{n} = \frac{7}{4} = \frac{14}{8}\]