NEET-XII-Physics
17: Light Waves
- #11White 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.Ans : 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 = `` \frac{m{\lambda }_{v}D}{d}``
Position of the nth bright fringe of red light, yr = `` \frac{n{\lambda }_{r}D}{d}``
For overlapping, yv = yr .
So, as per the question,
`` \frac{m\times 400\times \,\mathrm{\,D\,}}{d}=\frac{n\times 700\times \,\mathrm{\,D\,}}{d}``
`` \Rightarrow \frac{m}{n}=\frac{7}{4}``
Therefore, the `` {7}^{\,\mathrm{\,th\,}}`` 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, `` \frac{m}{n}=\frac{7}{4}=\frac{14}{8}``
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