Question

In a Young's double-slit experiment, two parallel slits with a slit separation of 0.135 mm are illuminated by light of wavelength 579 nm, and the interference pattern is observed on a screen located 4.15 m from the slits.

(a) What is the difference in path lengths from each of the slits to the location of the center of a fifth-order bright fringe on the screen?
µm

(b) What is the difference in path lengths from the two slits to the location of the center of the fifth dark fringe away from the center of the pattern?
µm

Answer 1

seperation between the slits, d = 0.135 mm

                                              = 0.135 * 10^-3 m

wavelength, ? = 579 nm

                      = 579 * 10^-9 m

distance between the screen to slits, L = 4.15 m

a)

The difference in path lengths from the two slits to the location of a fifth order bright fringe

on the screen is given by,

r = m

for the fifth order bright fringe, m = 5, then

path difference, r = 5*579*10^-9 m

r = 2.895 m

b)

The difference in path lengths from the two slits to the location of the fifth dark fringe on the screen, away from the

center of the pattern is given by,

r = (m + (1/2))

For the fifth order dark fringe, m = 4, then

path difference, r = (4 + 0.5)*(579 * 10^-9 )

r  = 2.605 m