White light is used in a young's double slit experiment. Find the minimum order of the vioet fringe $(λ = 400 n m)$ which overlaps with a red fringe $(λ = 700 n m .)$

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Solution

Let 'm' be the bright fringe of violet light overlaps with $n^{t h}$ bright fringe of red light.
$∴ \frac{m \times 400 n m \times D}{d} = \frac{n \times 700 n m \times D}{d} \Rightarrow \frac{m}{n} = \frac{7}{4}$
$\Rightarrow$ 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, $\frac{m}{n} = \frac{7}{4} = \frac{14}{8}$

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