White light is used in a Young's double slit experiment. Find the minimum order of the violet fringe $(\lambda=400\text{nm}),$ which overlaps with a red fringe $(\lambda=700\text{nm}).$
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Let $m^{th}$ bright fringe of violet light overlaps with $n^{th}$ bright fringe of red light.
$\therefore\frac{\text{m}\times400\text{nm}\times\text{D}}{\text{d}}=\frac{\text{n}\times700\text{nm}\times\text{D}}{\text{d}}\Rightarrow\frac{\text{m}}{\text{n}}=\frac{7}{4}$
$\Rightarrow 7^{\text {th }}$ bright fringe of violet light overlaps with $4^{\text {th }}$ bright fringe of red light (minimum). Also, it can be seen that $14^{\text {th }}$ violet fringe will overlap $8^{\text {th }}$ red fringe.
Because, $\frac{\text{m}}{\text{n}}=\frac{7}{4}=\frac{14}{8}$
$\therefore\frac{\text{m}\times400\text{nm}\times\text{D}}{\text{d}}=\frac{\text{n}\times700\text{nm}\times\text{D}}{\text{d}}\Rightarrow\frac{\text{m}}{\text{n}}=\frac{7}{4}$
$\Rightarrow 7^{\text {th }}$ bright fringe of violet light overlaps with $4^{\text {th }}$ bright fringe of red light (minimum). Also, it can be seen that $14^{\text {th }}$ violet fringe will overlap $8^{\text {th }}$ red fringe.
Because, $\frac{\text{m}}{\text{n}}=\frac{7}{4}=\frac{14}{8}$
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