1059
Chapter 33
Interference and Diffraction
Conceptual Problems
1
•
A phase difference due to pathlength difference is observed for
monochromatic visible light. Which phase difference requires the least
(minimum) path length difference? (
a
) 90
o
(
b
) 180
o
(
c
) 270
o
(
d
) the answer
depends on the wavelength of the light.
Determine the Concept
The phase difference
δ
due to a path difference
Δ
r
are
related according to
λ
π
r
Δ
=
2
. Therefore, the least path length difference
corresponds to the smallest phase difference.
( )
a
is correct.
2
•
Which of the following pairs of light sources are coherent: (
a
) two
candles, (
b
) one point source and its image in a plane mirror, (
c
) two pinholes
uniformly illuminated by the same point source, (
d
) two headlights of a car,
(
e
) two images of a point source due to reflection from the front and back surfaces
of a soap film.
Determine the Concept
Coherent sources have a constant phase difference. The
pairs of light sources that satisfy this criterion are (
b
), (
c
), and (
e
).
3
•
[SSM]
The spacing between Newton’s rings decreases rapidly as the
diameter of the rings increases. Explain qualitatively why this occurs.
Determine the Concept
The thickness of the air space between the flat glass and
the lens is approximately proportional to the square of
d
, the diameter of the ring.
Consequently, the separation between adjacent rings is proportional to 1/
d
.
4
•
If the angle of a wedgeshaped air film, such as that in Example 322 is
too large, fringes are not observed. Why?
Determine the Concept
There are two possible reasons that fringes might not be
observed.
(1) The distance between adjacent fringes is so small that the fringes
are not resolved by the eye. (2) Twice the thickness of the air space is greater than
the coherence length of the light.
If this is the case, fringes would be observed in
the region close to the point where the thickness of the air space approaches zero.
5
•
Why must a film that is used to observe interference colors be thin?
Determine the Concept
Colors are observed when the light reflected off the front
and back surfaces of the film interfere destructively for some wavelengths and
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1060
constructively for other wavelengths. For this interference to occur, the phase
difference between the light reflected off the front and back surfaces of the film
must be constant.
This means that twice the thickness of the film must be less
than the coherence length of the light. The film is called a thin film if twice its
thickness is less than the coherence length of the light.
6
•
A loop of wire is dipped in soapy water and held up so that the soap
film is vertical. (
a
) Viewed by reflection with white light, the top of the film
appears black. Explain why. (
b
) Below the black region are colored bands. Is the
first band red or violet?
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 Spring '12
 Goussiou
 Physics, Diffraction, Light, Wavelength, Thin Films, Substitute numerical values, Δr, mλ λ

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