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PHYS 222
Worksheet 33 – Interference and Phasors
Supplemental Instruction
Iowa State University
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
4/17/12
Useful Equations
L  r1  r2  m m  0, 1, 2...
d sin  m m  0, 1, 2...
1
d sin    m    m  0, 1, 2...

2
 
Constructive interference
Bring fringes
Dark fringes
 
Etotal  2E0 cos   cos t  Emax cos   cos t
2
 2
 

2
Time dependent E field at
point P
I P  I max cos2 
Intensity at point P
  k L  kd sin 
Phase difference
Diagrams
Phasors (two slits)
 
EP  2 E0 cos  
2
2
  k  r2  r1  
d sin 

(Phase difference related to
path difference)
Related Problems
1) Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits
waves with wavelength 6.00 m. Consider points along the line between the two sources.
(Book 35.1)
(a) At what distance from A is the interference constructive?
(b) At what distances from A is the interference destructive?
2) Two light sources can be adjusted to emit monochromatic light of any visible wavelength.
The two sources are coherent, 2.04 μm apart, and in line with an observer, so that one
source is 2.04 μm farther from the observer than the other. (Book 35.4)
(a) For what visible wavelengths (400 to 700 nm) will the observer see the brightest light,
owing to constructive interference?
(b) What would your answers to part (a) be if the two sources were not in line with the
observer, but were still arranged so that one source is 2.04 μm farther away from the
observer than the other?
(c) For what visible wavelengths will there be destructive interference at the location of the
observer?
3) Two slits spaced 0.460 mm apart are placed a distance of 75.5 cm from a screen. What
is the distance between the second and third dark lines of the interference pattern on the
screen when the slits are illuminated with coherent light with a wavelength of 530 nm?
(Book 35.9)
4) Coherent light with wavelength of 601 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 firstorder bright fringe is a distance of 4.84 mm from the center of the central bright fringe. For
what wavelength of light will the first-order dark fringe be observed at this same point on
the screen? (Book 35.15)
5) Coherent light with wavelength 510 nm passes through narrow slits with a separation
of 0.350 mm. At a distance from the slits which is large compared to their separation, what
is the phase difference (in radians) in the light from the two slits at an angle of 24.2
degrees from the centerline? (Book 35.21)
6) Points A and B are 62.0 m apart along an east-west line. At each of these points, a radio
transmitter is emitting a 13.0 MHz signal horizontally. These transmitters are in phase with
other and emit their beams uniformly in a horizontal plane. A receiver is
taken 0.550 km north of the AB line and initially placed at point C, directly opposite the
midpoint of AB. The receiver can be moved only along an east-west direction but, due to its
limited sensitivity, it must always remain within a range so that the intensity of the signal it
receives from the transmitter is no less than 1/4 of its maximum value. How far from
point C (along an east-west line) can the receiver be moved and always be able to pick up
the signal? (Book 35.25)