Question

A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. light waves arrive at the two slits in phase, and a fringe pattern is observed on a screen 4.8 m from the slits. if there are 6.0 complete bright fringes per centimeter on the screen near the center of the pattern, what is the wavelength of the monochromatic light?

Answer 1

For the bright fringes to appear the difference in the path traveled must be multiple of the wavelength:

`dsin(\theta)=m\lambda`
Using approximation when y is much smaller than L:

`sin(\theta)= (y)/(L)`
We get:

`y=(m\lambda L)/(d)`
Which means that distance between two bright fringes is:

`\Delta y= (\lambda L )/(d)`
We know that in our case the distance between two bright fringes is:

`\Delta y=(1cm)/(6)=0.166cm`

`\lambda=(\Delta y d)/(L)=6.2475\cdot10^(-7)m=624.75nm`