Question

In a Young's double-slit experiment, a set of parallel slits
with a separation of **0.104 mm** is illuminated by
light having a wavelength of **566 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 **fifth order** bright fringe on the
screen?

_________________________ *μ*m

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

_________________________ *μ*m

Answer #1

a) for mth bright fringe the distance will be x(bright) = m
(lambda) L / d

and since m = 5

so, the difference in path lengths from the two slits to the
location of a **fifth order** bright fringe on the
screen would be x2 = 5 x 566 x10^-9 x 3.5 / 0.104x10^-3 = 0.0952403
m = 95.2403 mm = 95240.3 um

b) the difference in path lengths from the two slits to the
location of the **fifth dark fringe**on the screen,
away from the center of the pattern

x(dark) = ( m+1/2) (lambda) L / d = (5+1/2) x 566 x10^-9 x 3.5 / 0.104x10^-3

= 0.1047644 m = 104.7644 mm = 104764.4 um

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