Question

In a Young's double slit experiment, the separation between the two slits is $0.9$mm and the fringes are observed one metre away. If it produces the second dark fringe at a distance of $1$mm from the central fringe, the wavelength of the monochromatic source of light used is?

• A. $450$nm
• B. $400$nm
• C. $500$nm
• D. $600$nm

Answer 1

Answer: (D)

$600$nm

The distance between two consecutive dark or bright fringes is recognised as $\beta$(fringe width) and that between central fringe and first dark fringe on either side is $\frac{\beta }{2}$.
Given, spacing between second dark fringe and central fringe $=\beta +\frac{\beta }{2}$
or $\frac{3\beta }{2}=1$mm (Given)
or $\beta =\frac{2}{3}\times 1$mm or $\frac{\lambda D}{d}=\frac{2}{3}mm$
$\therefore \lambda =\frac{2}{3}\times {10}^{-3}\times \frac{0.9\times {10}^{-3}}{1}$
$\Rightarrow \lambda =0.6\times {10}^{-6}$m
$\therefore$ Wavelength of the monochromatic source of light
$\lambda =600\times {10}^{-9}m=600$nm.