# Two slits are spaced 0.3mm apart and are placed 50cm from a screen, what is the distance between...

## Question:

Two slits are spaced 0.3mm apart and are placed 50cm from a screen, what is the distance between 2nd and 3rd dark pattern when alight of 600 nm

## Young's Double Slit Experiment

When monochromatic light passes through two slits which are spaced by a small distance then the light waves emerging from each slit superimpose with each other and forms a pattern of dark and bright bands, the distance between two consecutive dark or bright bands is known as fringe width. And the fringe width is given by

{eq}\begin{align} \beta = \frac{\lambda D}{d} \end{align} {/eq}

Where D is the distance of the screen from the slits, d is the separation between two slits and {eq}\lambda {/eq} is the wavelength of the light used.

Data Given

• The slit separation is {eq}d = 0.3 \ \rm mm = 0.3 \times 10^{-3} \ \rm m {/eq}
• Distance between the slits and the screen is {eq}D = 50 \ \rm cm = 0.50 \ \rm m {/eq}
• Wavelength of the light used {eq}\lambda = 600 \ \rm nm = 600 \times 10^{-9} \ \rm m {/eq}

The distance between 2nd and 3rd dark pattern is equal to the width of a bright fringe, so fringe width is given by

{eq}\begin{align} \beta = \frac{\lambda D}{d} \\ \beta = \frac{600 \times 10^{-9} \ \rm m \times 0.50 \ \rm m}{ 0.3 \times 10^{-3} \ \rm m} \\ \color{blue}{\boxed{ \beta = 0.001 \ \rm m = 1 \ \rm mm \ }} \end{align} {/eq}