Interference, Polarization and Color Review

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Part A: Multiple Choice

1. Which of the following statements are true statements about interference?

  1. Interference occurs when two (or more) waves meet while traveling along the same medium.
  2. Interference can be constructive or destructive.
  3. Interference of two waves at a given location results in the formation of a new wave pattern which has a greater amplitude than either of the two interfering waves.
  4. The meeting of a trough of one wave with a trough of another wave results in destructive interference.
  5. The only way for two waves to interfere constructively is for a crest to meet a crest or a trough to meet a trough.
  6. It is only a theory that light can interfere destructively; the theory is based on the assumption that light is a wave and most waves exhibit this behavior. Experimental evidence supporting the theory has not yet been observed.

 

Answer: AB

A - True: This is the definition of interference - "the meeting of two or more waves along the same medium."

B - True: These are the two possible types of interference.

C - False: When interference occurs, there are two possible results: a resulting wave with a greater displacement than either of the original waves (constructive interference) or a resulting wave with a smaller displacement than one or both of the original waves (destructive interference)

D - False: This is an example of constructive interference leading to a resulting wave with a greater displacement than the individual wave; a "super-trough" would be formed.

E - False: Crest meeting crest and trough meeting trough are examples of constructive interference. These special cases result in the formation of antinodal points - points of maximum displacement. But more generally, constructive interference will occur anytime a wave with a "positive" (up or right or ...) displacement meets another wave with a "positive" displacement OR when a wave with a "negative" (down or left or ...) displacement meets another wave with a "negative" displacement. When the displacements of the two interfering waves are in the same direction at a given point, then constructive interference occurs at that point.

F - False: There is plenty of experimental and observable evidence that light undergoes destructive interference. The best evidence from our studies in class are the dark fringes of a two-point interference pattern. These dark fringes are the result of the destructive interference of light.



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Interference of Waves | Two Point Source Interference


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2. Which of the following statements are true statements about two-point light source interference patterns?

  1. Two-point light source interference patterns consist of alternating nodal and antinodal lines.
  2. If projected onto a screen, two-point light source interference patterns would be viewed as alternating bright and dark spots with varying gradients of light intensity in between.
  3. As the distance between the sources is decreased, the distance between the nodal and antinodal lines is decreased.
  4. As the wavelength of the laser light is decreased, the distance between the nodal and antinodal lines is decreased.
  5. A nodal point would be formed if a trough of one wave meets a trough of another wave.
  6. Antinodal points are points where the medium is undergoing no vibrational motion.
  7. Suppose point P is a point where a wave from one source travels a distance of 2.5 wavelengths before meeting up with a wave from another source which travels a distance of 3.5 wavelengths. Point P would be a nodal point.
  8. Suppose point Q is a point where a wave from one source travels a distance of 2 wavelengths before meeting up with a wave from another source which travels a distance of 3.5 wavelengths. Point Q would be a nodal point.
  9. Suppose point R is a point where a wave from one source travels a distance of 2 wavelengths before meeting up with a wave from another source which travels a distance of 3 wavelengths. Point R would be a nodal point.
  10. If the path difference for points on the first nodal line is 4 cm, then the wavelength would be 6 cm. (NOTE: the first nodal line is considered to be the first nodal line to the left or right from the central antinodal line.)

Answer: ABDH

A - True: This is exactly what we have observed through computer animations, video segments, transparency overlays, and the actual experiment.

B - True: This is exactly what we observed when we performed Young's experiment.

C - False: The equation relating the variables of Young's experiment can be rearranged to the following form:

y = m • L • W / d ... (where W=wavelength).

Now one notices that y is inversely related to d. So if the slit separation distance (d) is decreased, the distance between nodal and antinodal lines (related to y) would be increased.

D - True: Young's equation is often written as

W = y • d / (m • L) ... (where W=wavelength).

From the equation, one notices that wavelength (W) is directly related to y. So if the wavelength (W) is decreased, the distance between nodal and antinodal lines (related to y) would be decreased.

E - False: Antinodal points are points of maximum displacement; for a light interference pattern, these are the brightest points.

F - False: Nodal points are points of no displacement or no disturbance; for a light light interference pattern, these are the darkest points.

G - False: In this case the path difference is 1 wavelength; when two waves traveling to the same point have a difference in distance traveled of 1 wavelength, then a crest of one wave would meet up with a crest of the second wave. This condition leads to constructive interference and an antinodal point is formed.

H - True: In this case the path difference is 1.5 wavelengths; when two waves traveling to the same point have a difference in distance traveled of 1.5 wavelengths, then a crest of one wave would meet up with a trough of the second wave. This condition leads to destructive interference and a nodal point is formed.

I - False: In this case the path difference is 1 wavelength; when two waves traveling to the same point have a difference in distance traveled of 1 wavelength, then a crest of one wave would meet up with a crest of the second wave. This condition leads to constructive interference and an antinodal point is formed.

J - False: The first nodal line is designated as m = 0.5; the path difference is 4 cm. Substituting into the equation PD = m•Wavelength and solving for wavelength yields a value of 8 cm.



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Two Point Source Interference


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3. Which of the following statements are true statements about nodal and antinodal points in light interference patterns?

  1. Antinodes result from constructive interference.
  2. Nodes result from destructive interference.
  3. The nodal points on an interference pattern are positioned along lines; these lines are called nodal lines.
  4. The central line on the interference pattern is a nodal line.
  5. Points on nodal lines would be represented by bright spots if projected onto a screen.
  6. The path difference for points on the central antinodal line would be 0.
  7. The path difference for points on the first antinodal line would be 1 cm.
  8. (This question presumes that the interference pattern is a water interference pattern.) If the path difference for points on the first antinodal line is 5 cm, then the path difference for points on the second antinodal line would be 7 cm.
  9. (This question presumes that the interference pattern is a water interference pattern.) If the path difference for points on the first antinodal line is 5 cm, then the path difference for points on the third antinodal line would be 15 cm.
  10. (This question presumes that the interference pattern is a water interference pattern.) If the path difference for points on the first antinodal line is 6 cm, then the path difference for points on the second nodal line would be 9 cm. (NOTE: the second nodal line is considered to be the second nodal line to the left or right from the central antinodal line.)
  11. (This question presumes that the interference pattern is a water interference pattern.) If the path difference for points on the first nodal line is 4 cm, then the path difference for points on the third nodal line would be 12 cm. (NOTE: the third nodal line is considered to be the third nodal line to the left or right from the central antinodal line.)

Answer: ABCFIJ

A - True: An antinode is a point where a crest meets a crest or a trough meets a trough; both are examples of constructive interference.

B - True: A node is a point where a crest meets a trough; this is an example of destructive interference and leads to a location of no displacement.

C - True: Nodal points all lie along lines. Question #21 illustrates this well.

D - False: The central line - that is, the line extending outward from the midpoint between the two sources - is a line upon which antinodes are formed; it is called an antinodal line. Question #21 illustrates this well.

E - False: Nodal lines are formed as a result of destructive interference. If projected onto a screen, the nodal points would appear as the darkest points on the interference pattern.

F - True: The path difference for points on the central antinodal line would be given be the equation: PD = m•W where W=wavelength and m=0 (for the central antinodal line). Substituting into this equation yields PD = 0•W which would be 0.

G - False: The path difference for points on the first antinodal line would be given be the equation: PD = m•W where W=wavelength and m=1 (for the first antinodal line). So the path difference for the first antinodal line would always be 1•W; but it would only be 1 cm for the case in which the wavelength is 1 cm.

H - False: The first antinodal line is numbered as the m=1 line. The path difference relates to the wavelength (W) by the equation PD = m•W. Substituting m=1 and PD=5 cm into this equation yields a wavelength value of 5 cm. The second antinodal line is numbered as the m=2 line. Re-using the equation for this line with m=2 and W=5 cm yields a path difference of 10 cm.

I - True: The first antinodal line is numbered as the m=1 line. The path difference relates to the wavelength (W) by the equation PD = m•W. Substituting m=1 and PD=5 cm into this equation yields a wavelength value of 5 cm. Re-using the equation for the third antinodal line with m=3 and W=5 cm yields a path difference of 15 cm.

J - True: The logic on this question is similar to the above question. The first antinodal line is numbered as the m=1 line. The path difference relates to the wavelength (W) by the equation PD = m•W. Substituting m=1 and PD=6 cm into this equation yields a wavelength value of 6 cm. The second nodal line is numbered as m=1.5. Re-using the equation for the second nodal line with m=1.5 and W=6 cm yields a path difference of 9 cm.

K - False: The first nodal line is numbered the m=0.5 line. If the path difference for a point on this line is 4 cm, then the wavelength is 8 cm (using the PD = m•W equation). The third nodal line is numbered as the m=2.5 line. Using the same equation to find the path difference yields a value of 20 cm.



Useful Web Links
Two Point Source Interference


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4. Which of the following statements are true statements about Thomas Young's experiment?

  1. Young's experiment provided evidence that light exhibits particle-like behavior.
  2. Young's experiment depends upon the use of white light from two sources.
  3. The two sources of light in Young's experiment could be two different light bulbs.
  4. For Young's equation to be geometrically valid, the distance from the sources to the screen must be much greater than the slit separation distance.
  5. For Young's equation to be geometrically valid, the wavelength of the light must be much greater than the slit separation distance.
  6. Thomas Young measured the distance from an antinodal point (of known number) to each of the two sources, computed a path difference and calculated the wavelength of light.
  7. Thomas Young was able to determine the wavelength of a light wave.

 

Answer: DG

a. - False: Young's experiment supports the wave-nature of light. Waves interfere and Young's experiment provided clear evidence that light undergoes interference.

b. - False: There are two requirements for the light which is utilized in Young's experiment: the two light sources must be coherent and monochromatic. Monochromatic means that the light sources must provide light of the same wavelength (and a single wavelength); using a white light bulb would produce light of many wavelengths. Second, coherent means that the light from the two sources must be vibrating together, experiencing a crest at the same time and a trough at the same time. Using two light bulbs (as opposed to a single light source shining on a double slit) would likely result in incoherent light.

c. - False: If two light bulbs emitting monochromatic light of the same color were used, one of the two requirements would be met. Yet there would still be the problem of incoherence. See explanation to part b.

d. - True: There are two geometric requirements for Young's experiment: the screen distance (L) must be much greater than the slit separation distance (d) and the slit separation distance must be much greater than the wavelength. That is L >>> d and d >>> W.

e. - False: Vice versa; d >>> W. See explanation to part d.

f. - False: Thomas Young used the equation W = y•d/m•L. Measurement of y, d, m, and L is much more practical since the size of these quantities is much larger. The error introduced in the measurement would not overwhelm the precision of the wavelength measurement. On the other hand, a measurement of the path difference would be very difficult since the only way to achieve this measurement is to measure the two distances. Given the fact that the slits are so close together, these two distances are so nearly identical that the error introduced in the measurement of one distance would overwhelm the actual difference in distance between the two measurements. That's why Young had to derive the equation W = y•d/m•L.

g. - True: Measuring the wavelength of a visible light wave was one of the main outcomes of Young's experiment.



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Two Point Source Interference


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5. Light which is vibrating in a single plane is referred to as _____ light

a. electromagnetic

b. transverse

c. unpolarized

d. polarized


Answer: D

Unpolarized light is light whose vibrations are in a multitude of directions. To simplify matters, unpolarized light is light which can be thought of as vibrating in a vertical and a horizontal plane. If one of these planes of vibration is removed, then light would be vibrating in a single plane and said to be "polarized."



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Polarization


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6. Light which is vibrating in a variety of planes is referred to as _____ light

a. electromagnetic

b. transverse

c. unpolarized

d. polarized


Answer: C

Unpolarized light is light whose vibrations are in a multitude of directions.



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Polarization


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7. Light usually vibrates in multiple vibrational planes. It can be transformed into light vibrating in a single plane of vibration. The process of doing this is known as ____.

a. translation

b. interference

c. polarization

d. refraction


Answer: C

Polarization is defined as the process of transforming unpolarized light (light whose vibrations are in a multitude of planes) into polarized light (light which can be thought of as vibrating in a single plane).



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Polarization


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8. Light is passed through a Polaroid filter whose transmission axis is aligned horizontally. This will have the effect of ____.

a. making the light one-half as intense and aligning the vibrations into a single plane.

b. aligning the vibrations into a single plane without any effect on its intensity.

c. merely making the light one-half as intense; the vibrations would be in every direction.

d. ... nonsense! This will have no effect on the light itself; only the filter would be effected.

Answer: A

Polaroid filters have the effect of polarizing light - that is, aligning their vibrations into a specific plane. They can be thought of as performing this feat by removing the vibrations which occur within a plane perpendicular to the transmission axis.



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Polarization


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9. Light is passed through a Polaroid filter whose transmission axis is aligned horizontally. It then passes through a second filter whose transmission axis is aligned vertically. After passing through both filters, the light will be ______.

a. polarized

 

b. unpolarized

 

c. entirely blocked

 

d. returned to its original state.


Answer: C

The first filter serves the role of blocking one-half the light; the horizontal vibrations would emerge from the filter and the vertical vibrations would be blocked. The second filter would allow the vertical vibrations to pass through if there were any. However, since the vertical vibrations have already been filtered out, there is no light remaining after the second filter is used. This combination of two filters serves to block all the light.



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Polarization


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10. Which of the following are effective methods of polarization? Include all that apply.

a. Passing light through a Polaroid filter.

b. Reflection of light off a nonmetallic surface.

c. Passing light from water to air.

d. Passing light through a birefringent material such as Calcite.

e. Turning the light on and off at a high frequency.

f. Interfering light from one source with a second source.

Answer: AB

The use of a filter, the reflection of light off nonmetallic surfaces and the use of a birefringent material are all means of polarizing light. Refraction at an air-water surface would change the speed and the direction of light but would not have any effect upon its vibrational orientation. Turning a light on and off at a high frequency would only annoy or impress those present in the room. And light interference could create a pattern of bright and dark spots but would not have any effect upon light's vibrational orientation.



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Polarization


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11. Consider the three pairs of sunglasses to the right. Which pair of glasses is capable of eliminating the glare from a road surface? (The transmission axes are shown by the straight lines.)

 

 


 

Answer: C

When light reflects off a road surface, a portion of the light vibrations becomes oriented in a plane which is horizontal to the road surface. This polarization often leads to an annoying glare. The glare can be reduced by blocking the polarized light. Since the light is polarized horizontally (assuming a horizontal road way - a good assumption), the sunglasses should be capable of blocking horizontal light and allowing the vertical vibrations to be transmitted. Selecting sunglasses C would make accomplish this feat.



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Polarization


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