Question

White light is used in a Young's double slit experiment. Find the minimum order of the violet fringe $(\lambda=400\, nm )$ which overlaps with a red fringe $(\lambda=700\, nm )$.

Answer 1

For violet light we have,
$y _{ v }=\frac{ n _{ v } \lambda_{ v }}{ d }$
For red light we have, $y_{r}=\frac{n_{r} \lambda_{r} D}{d}$
$\therefore$ For violet fringe to overlap with red fringe.
$y _{ v }= y _{ r }$
$\frac{ n _{ v } \lambda_{ v } D }{ d }=\frac{ n _{ r } \lambda_{ r } D }{ d }$
$\Rightarrow \frac{ n _{ v }}{ n _{ r }}=\frac{\lambda_{ r }}{\lambda_{ v }}=\frac{700}{400}$
$\frac{ n _{ v }}{ n _{ r }}=\frac{7}{4}=\frac{14}{8}$
$=\frac{21}{12}=\frac{28}{16}=\ldots \ldots . .$
$\therefore$ Minimum $7^{\text {th }}$ violet fringe overlaps with $4^{\text {th }}$ red fringe.