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± Fringes from Different Interfering Wavelengths

Coherent light with wavelength 592 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe.

Part A

For what wavelength of light will the first-order dark fringe (the first dark fringe next to a central maximum) be observed at this same point on the screen?

Express your answer in micrometers (not in nanometers).

ANSWER:

_______

?m

Answer 1

Young's double-slit experiment

path difference = d*sintheta

d*sintheta = m*lambda

for small angles

sintheta = tantheta = y/R

for bright fringe
------------------

path difference = m*lambda_1

d*y/R = m*lambda_1

y = m*lambda_1*R/d

d = slit width

m = order of bright fringe

R = distance between screen and slit

y = position of bright fringe on screen

for first bright

m = 1

y1bright = lambda_1/*R/d

at the same y if dark fringe forms for wavelength lambda 2

for dark fringe
----------------

path difference = (m+1/2)*lambda_2

d*y/R = (m+1/2)*lambda_2

y = (m+1/2)*lambda_2*R/d

for first dark

m = 0

y1dark = lambda_2*R/(2d)

y1bright = = y1dark

lambda_1*R/d = lambda_2*R/(2d)

lambda_2 = 2*lambda_1