Question

In Young's double slit experiment, separation between the slits is $2\times 10^{-3}m$ and distance of the screen from the slit is $2.5m$. Light in the range of $2000-8000\mathring{A}$is allowed to fall on the slits. Find the wavelength (in $\mathring{A}$) in the visible region that will be present on the screen at $10^{-3}m$ from the central maxima will be______.

Answer 1

Answer: 4000

Path difference at a distance $x$ from the central maxima on screen is given as
$\Delta =\frac{xd}{D}=\frac{10^{-3}\times 2\times 10^{-3}}{2.5}=8000\mathring{A}$
For bright line at this position, we use
$8000=n_1{\lambda }_1$ If $n_1=2$, we get ${\lambda }_1=4000\mathring{A}$
Thus second bright line for visible region is present.