In a Young\'s double-slit experiment, two parallel slits with a slit separation

Question

In a Young's double-slit experiment, two parallel slits with a slit separation of 0.155 mm are illuminated by light of wavelength 599 nm, and the interference pattern is observed on a screen located 3.90 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?


(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?

Explanation / Answer

Given: slits seperation d = 0.155 m m = 0.155 x10-3 m wavelength = 589 nm = 599 x 10 -9 m distance between the screen to slits   D = 3.9 m ( a) for 5 th order bright fringe path difference  = m    where m = 5 thus, r = difference in path lengths from each of the slits               = 5 (599 x 10 -9 m)               = 2995 x 10 -9 m                                             (b) r = (4.5)( 599 x 10 -9 m )            = 2695.5 x  x 10 -9 m

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