Green light of a certain wavelength is incident upon two slits separated by 2.10 \times 10^{-5}...

Question:

Green light of a certain wavelength is incident upon two slits separated by 2.10 \times 10^{-5} m. A screen is placed 0.800 m from the slits. The distance from the central bright line to the first-order line is 19.9 mm. What is the wavelength of the light?

Wavelength of light

Light behaves like waves and when it passes through the two slits placed closed to each other, two waves are created. When these waves fall on a screen in sync, then a bright fringe is created and when they fall out of sync then a dark fringe is created.

The screen is placed at a distance of L = 0.8 m, from the slits and the slits are separated by a distance of {eq}\rm d = 2.1 \times 10^{-5} \ m {/eq}

Distance between the central bright fringe to the first order fringe is given as:

{eq}\rm y = \dfrac{\lambda L}{d} {/eq}

{eq}\rm 19.9 \times 10^{-3}= \dfrac{\lambda \times 0.8}{2.1 \times 10^{-5}} {/eq}

{eq}\rm \lambda = \dfrac{2.1 \times 10^{-5} \times 19.9 \times 10^{-3}}{0.8} {/eq}

{eq}\rm \lambda = 522.4 \times 10^{-9} \ m = 522.4 \ nm {/eq}