Question

Two slits spaced 0.455 mm apart are placed 50.0 cm from a screen. What is the distance between the second and third dark lines of the interference pattern on the screen when the slits are illuminated with coherent light with a wavelength of 540 nm?

mm

Answer 1

Young's double-slit experiment

path difference = d*sintheta

for dark line

path difference = (m + 1/2)*lambda

d*sintheta = (m + 1/2)*lambda

for small angles sintheta = tantheta = y/R

d*y/R = (m + 1/2)*lambda

y = (m + 1/2)*lambda*R/d

d = slit width

m = order of dark line

R = distance between screen and slit

y = position of bright fringe on screen

for m = 1 ( secon dark)

y2 = (3/2)*lambda*R/d

for m = 2 ( third dark)

y3 = (5/2)*lambda*R/d

distance between y3 and y2 , dy = y3 - y2

dy = lambda*R/d

dy = 540*10^-9*0.5/(0.455*10^-3)

dy = 0.593 mm <<<<<-----------ANSWER