Question

In Young's double-slit experiment, the slits are $2mm$ apart and are illuminated with a mixture of two wavelength $\lambda _{1}=750nm$ and $\lambda _{2}=900nm$ . The minimum distance from the common central bright fringe on a screen $2m$ from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other is:

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

Answer 1

Answer: (C)

$n_{1}\lambda _{1}=n_{2}\lambda _{2}$
$n_{1}\times 750\times 10^{- 9}=n_{2}\times 900\times 10^{- 9}$
$\frac{n_{1}}{n_{2}}=\frac{6}{5}n_{1}=6,n_{2}=5$
$x_{1}=\frac{n_{1} D \lambda _{1}}{ d}$
$x_{1}=\frac{6 \times 2 \times 750 \times 10^{- 9}}{2 \times 10^{- 3}}$
$x_{1}=4.5mm$