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

Question

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.150 mm is illuminated by light having a wavelength of 586 nm and the interference pattern observed on a screen 4.50 m from the slits.

(a) What is the difference in path lengths from the two slits to the location of a third order bright fringe on the screen?
_____ µm
(b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?
_____ µm

Explanation / Answer

Here ,

seperation , d = 0.150 mm

wavelength = 586 nm

screen distance , D = 4.5 m

a) for the thid order bright fringes

difference in paths = 3 * wavelength

difference in paths = 3 * 586 *10^-9

difference in paths = 1.758 *10^-6 m

the difference in path lengths from the two slits to the location of a third order bright fringe on the screen is 1.758 *10^-6 m

b)

for the location of third dark fringe

m = 2.5

difference in paths = 2.5 * wavelength

difference in paths = 2.5 * 586 *10^-9

difference in paths = 1.456 *10^-6 m

the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern is 1.456 *10^-6 m

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