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.