# a) Two narrow slits are illuminated by a laser with a wavelength of 583 nm. The interference...

## Question:

a) Two narrow slits are illuminated by a laser with a wavelength of 583 nm. The interference pattern on a screen located x = 5.20 m away shows that the fourth-order bright fringe is located y = 7.00 cm away from the central bright fringe. Calculate the distance between the two slits.

b) The screen is now moved 1.4 m further away. What is the new distance between the central and the fourth-order bright fringe?

## Interference

Interference is defined as the superimposition of the wavefront which creates the bright and dark fringes. When the extra distance traveled path by the wave is equal to the integral multiple of wavelength then the constructive interference takes place.

(a)

Given

The wavelength of the light {eq}\lambda = 583 \ nm {/eq}

Distance of the screen (x) = 5.2 m

Now, the bright fringe is given by

{eq}\dfrac{dy}{x} = m\lambda \\ \dfrac{d*0.07}{5.2} = 4*583*10^{-9} \\ d = 1.73*10^{-4} \ m {/eq}

Where

• d is the distance between the slits
• m is the order of the fringe

(b)_

Now the distnace of the screen (x) = 5.2 + 1.4 = 6.6 m

Therefore

{eq}\dfrac{dy}{x} = m\lambda \\ \dfrac{1.73*10^{-4}*y}{6.6} = 4*583*10^{-9} \\ y =8.897 \ cm {/eq}