Question

"White light is used in a Young’s double slit experiment. Find the minimum order of the violet fringe
λ=400 nmwhich overlaps with a red fringe λ=700 nm."

Answer 1

Hey ✌️

✨Gud Mrng ✨

____________________________

Answer:

Let mth bright fringe of violet light overlaps with nth bright fringe of red light.

=> 7th bright fringe of violet light overlaps with 4th bright fringe of red light (minimum).

Also, it can be seen that 14th violet fringe will overlap 8th red fringe. Because, m/n = 7/4 = 14/8.

Answer 2

Given :

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

Suppose, the mth bright fringe of violet light overlaps with the nth bright fringe of red light.

Now, the position of the mth bright fringe of violet light, yv = mλvD/d

For overlapping, yv = yr . [according to the question]

m×400×D/d=n×700×D/d⇒m/n=7/4

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

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

Because,

m/n=7/4=14/8