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 0.102 mm is illuminated by light having a wavelength of 575 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 fourth order bright fringe on the screen?

___ m

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

___m

Explanation / Answer

here d = 0.102 mm = 0.102 x 10-3 m lemda = 575 nm = 575 x 10-9 m L = 3.50 m

m = 4

(a) for the bright fringes

as we know that

lemda = yd / mL

y = mL (lemda) / d

= ( 4 x 3.50 x 575 x 10-9 ) / ( 0.102 x 10-3 )

= 0.07892 m = 78921.5686 um Ans

(b) for the dark fringes

lemda = yd / (m+1/2) L

y = (4+0.5) x 3.50 x 575 x 10-9 ) / ( 0.102 x 10-3 )

y = 88786.7647 um Ans

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