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

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

Tardigrade Admin · Accepted Answer

The distance between two consecutive dark or bright fringes is recognised as

β

(fringe width) and that between central fringe and first dark fringe on either side is

\frac{β}{2}

.
Given, spacing between second dark fringe and central fringe

= β + \frac{β}{2}

or

\frac{3 β}{2} = 1 mm

(Given)
or

β = \frac{2}{3} \times 1 mm

or

\frac{λ D}{d} = \frac{2}{3} mm

∴ λ = \frac{2}{3} \times 1 0^{- 3} \times \frac{0.9 \times 1 0 ^{- 3}}{1}

\Rightarrow λ = 0.6 \times 1 0^{- 6} m

∴

Wavelength of the monochromatic source of light

λ = 600 \times 1 0^{- 9} m = 600 nm

.

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

500 nm

600 nm

450 nm

400 nm

Q. 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