Question

In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths ${\lambda }_1=12000A^0$ and ${\lambda }_2=10000A^0$. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

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

Answer 1

The correct option is B 6 mm

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{n_2}{n_1}=\frac{12000}{10000}=\frac{6}{5}$
$x=\frac{n_1{\lambda }_{1}D}{d}=\frac{5\times 12000\times {10}^{-10}\times 2}{2\times {10}^{-3}}$
$=6mm$