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Example Question #1151 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
The experiment is repeated on a vehicle moving with a constant velocity at 100 mph. Why should we expect the data to remain the same?
The extra length traveled by each light beam is offset by the reduced time spent at each location.
The interference fringes themselves are affected by the motion of the screen due to the velocity of the vehicle.
The motion of the vehicle exactly cancels out the speed of light.
According to the special theory of relativity, the speed of light is the same for an observer moving with constant velocity as it is for a stationary observer.
According to the special theory of relativity, the speed of light is the same for an observer moving with constant velocity as it is for a stationary observer.
Since a student inside the vehicle would observe that light's velocity is the same, there would be no changes in how it behaves within the fiber-optic interferometer.
Example Question #1152 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
In this experiment, the student used 632 nm light. For small changes in optical path difference, which wavelength of light would be the best?
460 nm
800 nm
632 nm
1064 nm
460 nm
According to the equation
we want a small wavelength in order to maximize the number of fringe shifts we observe. This is desirable for small changes that might not be easily measurable.
Example Question #1153 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
The experiment is set up such that both beam paths have the same length. What would be the effect of doubling the path length for both of the beam paths?
There would be no discernable effect on the number of fringe shifts.
There would be twice as many fringe shifts.
There would be half as many fringe shifts.
There would be higher optical path difference.
There would be no discernable effect on the number of fringe shifts.
In the following equation
Example Question #1154 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
Suppose the student conducted the experiment with 632 nm light. What would happen to the measured fringe shifts if 1064 nm light were used instead?
The fringe shifts would be divided by 1.7.
The fringe shifts would be multiplied by 3.4
The fringe shifts would be divided by 3.4.
The fringe shifts would be multiplied by 1.7.
The fringe shifts would be divided by 1.7.
If 1064 nm light is used instead, the new 
According to the equation,
Multiplying 
Example Question #1155 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
One way optical fibers can contract and expand is through thermal changes. According to the data, what is the effect of increasing the voltage drop through a resistor?
The increased voltage leads to a greater decrease in the speed of light.
The increased voltage allows for more efficient electric transmission.
The increased voltage leads to higher power dissipation.
The increased voltage does not affect the experimental data.
The increased voltage leads to higher power dissipation.
Temperature changes depend on how much power is dissipated through a resistor. The data show that having a higher voltage leads to more optical path change, which implies greater power dissipation.
Example Question #1156 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below. Uncertainties are given in parentheses next to the measured values.
The optical path is related not only to the physical distance, but to the index of refraction of the medium.
The velocity of light 
where 
Suppose the student measures a higher index of refraction 
What does this finding imply about the travel time of a photon passing through fiber 2?
The photon would take the same time to reach the screen.
The photon would take a shorter time to reach the screen.
The photon would take a longer time to reach the screen.
The photon's transit time would depend on its initial velocity.
The photon would take a shorter time to reach the screen.
We have the following equation for photon speed in fiber 1:
The photon speed in fiber 2 is given by:
The index of refraction for fiber 2, which we denote as 
A greater speed means shorter transit time for the photon in fiber 2.
Example Question #1157 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
What is one valid hypothesis for why fanning the air near a fiber optic cable should cause 0.5 fringe shifts in the student's experiment?
The air introduces disturbances into the optics of the light source, leading to diffraction patterns.
The air's motion causes refraction of the beam, thereby distorting the interference pattern observed on the screen.
The air changes how the light is coupled into the fiber-optic cables by the lens.
The air cools or heats one of the fiber optic cables more than the other, causing it to shrink or expand.
The air cools or heats one of the fiber optic cables more than the other, causing it to shrink or expand.
The only explanation that is consistent with the idea that the optical path changes cause fringe shifts is that one fiber shrinks or contracts more than the other. Therefore, the air is most likely causing a temperature-induced contraction or expansion.
Example Question #1158 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
Why would a standard halogen flashlight not be a good choice of light source in this experiment? Choose the answer that represents the greatest drawback.
The flashlight would reflect poorly off of the beam splitter.
The flashlight would cause excessive heating in the fiber cables.
The flashlight emits light waves that are not coherent.
The flashlight would not be visible on the screen after recombination.
The flashlight emits light waves that are not coherent.
As stated in the question statement, our requirement for the light source is that it emits coherent light. A laser is an example that meets this requirement. A standard flashlight is not designed to meet this requirement.
Example Question #1159 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
Why might fiber-optic cables be used instead of mirrors to redirect the beams? Consider the following scenarios and determine which one would motivate the choice of fiber-optic cables rather than mirrors.
The interferometer must be used in a miniature deformable device to detect temperature-induced expansion.
The interferometer must be used to measure the speed of sound.
The interferometer must be used to measure changes in orbital distance between the moon and the Earth.
The interferometer must be used to measure the speed of light.
The interferometer must be used in a miniature deformable device to detect temperature-induced expansion.
The fiber-optic cables enable the optical paths to be easily arranged, which make them ideal for applications in smaller devices. Any experiment in which the interferometer is used to measure extremely long distances (e.g. speed of light, distance between two astronomical bodies) would be a poor use for fiber optics. Imagine the cost of a 100,000 mile fiber-optic cable!
Example Question #1160 : Act Science
A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.
By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:
where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and 
Experiment 1:
A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.
Why is it necessary to use a second beam splitter in this setup?
The first beam splitter reduces the intensity of the light, which must be compensated for.
The second beam splitter acts as a screen on which interference fringes can be observed.
The beams must be recombined so that interference fringes are observed.
The beams must be refocused since they are exiting from different points.
The beams must be recombined so that interference fringes are observed.
The second beam splitter recombines two beams. The interference fringes are only visible if the two beams are superimposed, as the question statement describes.
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