# If the distance between two slits is 0.05 mm and the distance to the screen is 2.5 m, find the...

## Question:

If the distance between two slits is 0.05 mm and the distance to the screen is 2.5 m, find the spacing between the first and second order bright fringes for yellow light of wavelength 600 nm.

## Spacing of fringes

For a bright fringe in an interference pattern produced on a screen at distance L from the slits separated by distance d, the distance from the central maxima is given as:

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

where {eq}\rm m = order \ of \ fringe {/eq}

Given:

• Wavelength of yellow light = {eq}\lambda = 600 \ nm = 600 \times 10^{-9} \ m {/eq}
• Distance of the screen from the slits = L = 2.5 m

Spacing of the slits = d = 0.05 mm = {eq}\rm 0.05 \times 10^{-3} \ m {/eq}

• The distance of the first bright fringe from the central maximum is:

{eq}\rm y_1 = \dfrac{\lambda L}{d} {/eq}

The distance of the second bright fringe from the central maximum is:

{eq}\rm y_2 = \dfrac{2 \lambda L}{d} {/eq}

Then spacing between the first and second bright fringe is:

{eq}\rm \Delta y = y_2 - y_1 {/eq}

{eq}\rm \Delta y = \dfrac{2 \lambda L}{d} - \dfrac{ \lambda L}{d} {/eq}

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

{eq}\rm \Delta y = \dfrac{ 600 \times 10^{-9} \times 2.5}{0.05 \times 10^{-3}} {/eq}

{eq}\rm y = 0.03 \ m = 3 \ cm {/eq}