Worksheet 33 – Interference and Phasors
Supplemental Instruction
Iowa State University / Leader: / Alek Jerauld
Course: / PHYS 222
Instructor: / Dr. Paula Herrera-Siklódy
Date: / 4/17/12
Useful Equations
Constructive interference
Bring fringes
Dark fringes
Time dependent E field at
point P
Intensity at point P
Phase difference
DiagramsPhasors (two slits)
(Phase difference related to path difference)
Related Problems
1)Two coherent sourcesAandBof radio waves are 5.00mapart. Each source emits waves with wavelength 6.00m. Consider points along the line between the two sources. (Book 35.1)
(a) At what distance fromAis 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 μmapart, and in line with an observer, so that one source is2.04 μmfarther from the observer than the other. (Book 35.4)
(a) For what visible wavelengths (400 to 700nm) 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 is2.04 μmfarther away from the observer than the other?
(c) For what visible wavelengths will there bedestructiveinterference at the location of the observer?
3) Two slits spaced0.460mmapart are placed a distance of75.5cmfrom 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 of530nm? (Book 35.9)
4) Coherent light with wavelength of601nmpasses through two very narrow slits and the interference pattern is observed on a screen a distance of3.00mfrom the slits. The first-order bright fringe is a distance of4.84mmfrom 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 wavelength510nmpasses through narrow slits with a separation of0.350mm. 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 of24.2 degreesfrom the centerline? (Book 35.21)
6) PointsAandBare62.0mapart along an east-west line. At each of these points, a radio transmitter is emitting a13.0MHzsignal horizontally. These transmitters are in phase with other and emit their beams uniformly in a horizontal plane. A receiver is taken0.550kmnorth of theABline and initially placed at pointC, directly opposite the midpoint ofAB. 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 than1/4of its maximum value. How far from pointC(along an east-west line) can the receiver be moved and always be able to pick up the signal? (Book 35.25)