Question

In Young's double slit experiment, the slits are 2mm apart and are illuminated by photons of two wavelengths ${\lambda }_1=12000\mathring{A}$ and ${\lambda }_2=10000\mathring{A}.$ At what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

• A. 3 mm
• B. 8 mm
• C. 6 mm
• D. 4 mm

Answer 1

Answer: (C)

According to question $n_1{\lambda }_1=n_2{\lambda }_2$
So $\frac{n_1}{n_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{10000}{12000}=\frac{5}{6}$
so minimum $n_1$ and $n_2$ are 5 and 6 respectively
$X_{min}=\frac{n_1{\lambda }_{1}D}{d}=\frac{5(12000\times 10^{-10})(2)}{2\times 10^{-3}}$
$=6\times 10^{-3}m=6mm$