Question

The separation between the consecutive dark fringes in a Young's double slit experiment is 1.0 mm. The screen is placed at a distance of 2.5m from the slits and the separation between the slits is 1.0 mm. Calculate the wavelength of light used for the experiment.

Answer 1

Given:-

Separation between consecutive dark fringes = fringe width (β) = 1 mm = 10⁻³ m

Distance between screen and slit (D) = 2.5 m

The separation between slits (d) = 1 mm = 10⁻³ m

Let the wavelength of the light used in experiment be λ.

We know that

$$\beta =\frac{\lambda D}{d}$$

$${10}^{-3}m=\frac{2.5\times \lambda }{{10}^{-3}}$$

$$\Rightarrow \lambda =\frac{1}{2.5}{10}^{-6}m$$

$$=4\times {10}^{-7}m=400\text{ nm}$$

Hence, the wavelength of light used for the experiment is 400 nm.