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

Answer 1

Answer: (B)

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 $\frac{3 \beta}{2}=1 mm \quad$ (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
$\lambda=600 \times 10^{-9} m =600 nm$.