Question

In a Young's double - slit experience, the slits are 2mm apart and are illuminated with a mixture of two wavelengths ${\lambda }_0=750nm$ and $\lambda =900nm$. The minimum distance from the common central bright fringe on a screen 2 m away from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other, is

• A. 1.5mm
• B. 3 mm
• C. 4.5 mm
• D. 6 mm

Answer 1

The correct option is C 4.5 mm

$y_0=n\left[\frac{D\lambda }{d}\right]$ and $y_n^{\prime }=n^{\prime }\left(\frac{D{\lambda }^{\prime }}{d}\right)$
Equating $y_n$ and $y_n^{\prime }$,we get
$\frac{n}{n^{\prime }}=\frac{{\lambda }^{\prime }}{\lambda }=\frac{900}{750}=\frac{6}{5}$
Hence, the first position at which overlapping occurs is
$y_6=y_6=\frac{6\left(2\right)(750\times {10}^{-9})}{2\times {10}^{-3}}=4.5mm$