# A laser beam is incident on two slits with a separation of 0.210 mm, and a screen is placed 5.10...

## Question:

A laser beam is incident on two slits with a separation of {eq}0.210\ mm {/eq}, and a screen is placed {eq}5.10\ m {/eq} from the slits. An interference pattern appears on the screen. If the angle from the center fringe to the first bright fringe to the side is {eq}0.187 ^\circ {/eq}, what is the wavelength of the laser light?

## Wavelength of light

The light after passing through the two slits behaves as a wave and produces an interference pattern on the screen. There are alternate bright and dark bands with a central bright fringe. The bright fringes are due to constructive interference and dark ones are due to destructive interference.

The separation between the slits is given as {eq}\rm d = 0.21\ mm = 0.21 \times 10^{-3} \ m {/eq}

The angle between centre fringe to the first bright fringe to the side is {eq}\rm \theta = 0.187 ^{\circ} {/eq}

Let {eq}\lambda {/eq} be the wavelength of the incident light.

For constructive interference:

{eq}\rm dsin(\theta) = m\lambda {/eq}

{eq}\rm \lambda = \dfrac{dsin(\theta)}{m} {/eq}

{eq}\rm \lambda = \dfrac{0.21 \times 10^{-3} \times sin(0.187)}{1} {/eq}

{eq}\rm \lambda = 685.4 \times 10^{-9} \ m = 685.4 \ nm {/eq}