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 $2.5 \,m$. 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

Path difference at a distance $x$ from the central maxima on screen is given as
$\Delta=\frac{x d}{D}=\frac{10^{-3} \times 2 \times 10^{-3}}{2.5}=8000\,\mathring{A}$
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.