Question

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.104 mm is illuminated by light having a wavelength of 566 nm and the interference pattern observed on a screen 3.50 m from the slits.

(a) What is the difference in path lengths from the two slits to the location 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 fifth dark fringe on the screen, away from the center of the pattern?

_________________________ μm

Answer 1

a) for mth bright fringe the distance will be x(bright) = m (lambda) L / d

and since m = 5

so, the difference in path lengths from the two slits to the location of a fifth order bright fringe on the screen would be x2 = 5 x 566 x10^-9 x 3.5 / 0.104x10^-3 = 0.0952403 m = 95.2403 mm = 95240.3 um

b) the difference in path lengths from the two slits to the location of the fifth dark fringeon the screen, away from the center of the pattern

x(dark) = ( m+1/2) (lambda) L / d = (5+1/2) x 566 x10^-9 x 3.5 / 0.104x10^-3

= 0.1047644 m = 104.7644 mm = 104764.4 um