Question

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

Answer 1

Answer: 7.00

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.
$y_v=y_r$
$\frac{n_v{\lambda }_{v}D}{d}=\frac{n_r{\lambda }_{r}D}{d}$
$\Rightarrow \frac{n_v}{n_r}=\frac{{\lambda }_r}{{\lambda }_v}=\frac{700}{400}$
$\frac{n_v}{n_r}=\frac{7}{4}=\frac{14}{8}$
$=\frac{21}{12}=\frac{28}{16}=\dots \dots ..$
$\therefore$ Minimum $7^{\text{th }}$ violet fringe overlaps with $4^{\text{th }}$ red fringe.