PHYS 201 Review Exercises for Midterm 2
1.
An interference pattern is produced by light with a wavelength 570
from a distant source incident on
two identical parallel slits separated by a distance (between centers) of 0.520 mm.
a. If the slits are very narrow, what would be the angular position of the firstorder, twoslit, interference
maxima?
b. What would be the angular position of the secondorder, twoslit, interference maxima in this case?
c. Let the slits have a width 0.330 mm. In terms of the intensity
at the center of the central maximum,
what is the intensity at the angular position in part (a) ?
d. What is the intensity at the angular position in part (b) ?
Solution:
Visualize (i.e. Draw!): Does the image in your mind look anything like below ?
θ
a
a
Understand what is given:
distance between slits d = 0.520 mm
d
λ
= 570 nm
slit width a is either very small
in part (a,b) or a = 0.33nm in
part (c,d).
(a).
In (a,b), the slits are assumed to be narrow – what does this mean ?
It means the cental maximum “envelope” is smeared across the whole screen (Diffraction
minima are given by a sin
θ
= m
λ
. For a fixed
λ
, small “a” means sin
θ
is big (say, 1.0) so
θ
= 90° and
the diffraction minima are at +/ infinity. This means the interference pattern will not be affected by
diffraction. This is contrast to parts c,d
where the slit width is then finite (bigger than zero) and so the
diffraction minima will be squeezed towards the center. Note that widening the slit translates into
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 Spring '10
 dodge
 Diffraction, Wavelength, interference fringes

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