Question

Two narrow slits are illuminated by a laser with a wavelength of 522 nm. The interference pattern on a screen located x = 4.80 m away shows that the third-order bright fringe is located y = 9.10 cm away from the central bright fringe. Calculate the distance between the two slits.

The screen is now moved 0.9 m further away. What is the new distance between the central and the third-order bright fringe?

Answer 1

The position of the bright fringe is given by the equation

Where

n = order of fringe = 3

x_n = position of n=3 fringe = 9.1 cm = 0.091 m

d = distance between the two slits

D = Distance between screen and slit = 4.8 m

= wavelength = 522 nm = 522 x 10^-9 m  

So, d =   (3 x 522 x 10^-9 x 4.8 )/0.091 m = 8.26 x 10^-5 m

Now

New distance between the screen and slit = 4.8 + 0.9 m = 5.7 m

Hence, x_n = (3 x 522 x 10^-9 x 5.7 )/(8.26 x 10^-5 ) m = 0.108 m

So,

Distance between the slits is 8.26 x 10^-5 m -------------------(a)

New distance between central and third order fringe is 0.108 m ---------------------(b)