Chapter 27: Wave Interference Key
Example Problems
c  f
n
c
v mat
  sin   tan  
y
L


mat
  dsin m  m, m  0, 1, 2,...
ym  mL/d
ym  (m  21 )L/d
m /n
2t  
1
(m  2 ) /n
Example 27.1
The two waves in the figure have wavelengths of  = 500 nm in air. What
is the phase difference acquired when wave-1 and wave-2 emerging from
(a) (n1 = 1.50, n2= 1.60) and (b) (n1 = 1.59, n2 = 1.86)? (c) Draw a picture
of the wave paths for (a) and (b), and determine the m-value (d) Are the
waves interfering constructively, destructively or neither? Explain your reasoning.
Example 27.2
Light from a helium-neon laser (λ = 633 nm) is used to illuminate two narrow slits. The
interference pattern is observed on a screen 3.0 m behind the slits. Twelve bright fringes
are seen, spanning a distance of 52 mm. (i) Sketch the interference pattern in detail. (ii)
What is the spacing (in mm) between the slits?
Example 27.3
In a double-slit experiment, the distance between slits is 5.0 mm and the slits are 1.0 m
from the screen. Two interference patterns can be seen on the screen: one due to light
of wavelength 480 nm, and the other due to light of wavelength 600 nm. (a) Is the small
angle approximation valid in this situation? (b) (i) What is the separation on the screen
between the third-order bright fringe of 480 nm light and the third-order dark fringe of
600 nm light? (ii) Draw a picture of the situation. (c) Do the 480 nm and 600 nm light
waves interfere with each other on the screen? Explain your reasoning.
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Example 27.4
Solar cells are given antireflection coatings to maximize their efficiency. Consider a
silicon solar cell (n = 3.50) coated with a layer of silicon dioxide (n = 1.45). What is the
minimum coating thickness that will minimize the reflection at the wavelength of 700 nm,
where solar cells are most efficient?
Example 27.5
A disabled tanker leaks kerosene (n = 1.20) into the Persian Gulf, creating a large slick
on top of the water (n =1.30). (a) If you are looking straight down from an airplane, while
the Sun is overhead, at a region of the slick where its thickness is 460 nm, for which
wavelength(s) of visible light is the reflection brightest because of constructive
interference? (b) If you are scuba diving directly under this same region of the slick, for
which wavelength(s) of visible light is the transmitted intensity strongest?
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