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Official Physics Quiz

INTERFERENCE AND DIFFRACTION OF LIGHT

This booklet contains 20 multiple choice questions worth 1 point each. Use the Scantron sheet supplied as your answer sheet. If you wish to you may use scratch paper and a computation aid (i.e., a calculator, slide rule, abacus, or perhaps even a brain). Otherwise this quiz is closed book, closed notes, and definitely closed neighbor. Do NOT mark on this booklet in any way. If you do, a humongous horde of handsome, hairless hottentots will hustle you to Hollywood for a public humiliation.

When you finish the quiz, put your answer sheet inside this booklet and place the booklet on Mr. McGehee's desk in the front of the room in the version A or version B pile.

934

Equations - Chapter 19 Quiz

10-9 meter = 1 nanometer

f = 1/Tv = /T = fvlight = 3 x 108 m/s

 = xd/L or  = xd/L = d sin 

 = xw/L = w sin 

 = xd/L = d sin 

1

General Waves, INTERFERENCE AND DIFFRACTION OF LIGHT

1.On Planet X, two tuning forks are side-by-side making sound. One is pitched at 500 Hz with a wavelength of 2.5 m. The other is pitched at 2500 Hz. Call the first one wave A and the second one wave B.

  1. Find the speed of wave A.
  2. Find the speed of wave B.

2. A yellowish-green color has a wavelength of 550 nm. Find the frequency that generated this color.

3. A source of light contains all possible categories of electromagnetic waves, not just the visible category. In an experiment, astronauts in space shine this light vertically onto a surface that is covered with a layer of air that is precisely 600 nm thick. The light travels from the vacuum of space through the layer of air and reflects off of the solid surface that is behind the air layer. When the light originally travels from vacuum to the air layer, it partially reflects off the initial surface of the air layer and it partially passes through. The part that makes it through travels to the solid surface where there is full reflection. Both the reflections off of the air layer and off of the solid surface invert the wave.

Note: The index of refraction of air is very close to 1, so light wavelengths in air are about the same as they are in vacuum.

Any questions below that ask about reflected light are referring to what is observed in the sum total of all the reflected light that comes off of this air/surface complex.

  1. Calculate the longest wavelength that can exist in the total of the reflected light.
  2. Calculate the second longest wavelength that can exist in the total of the reflected light.
  3. Calculate the third longest wavelength that can exist in the total of the reflected light.
  4. Come up with a value of an air layer thickness that would only allow ONE possible visible color in the total reflected light.
  5. Excluding any of the answers you gave to A, B, or C, what other possible categories of the EM spectrum could exist in the total reflected light?

4. Suppose a standing wave generator produces waves in the space between a piston and a rigid boundary that is located 1.8 m away from the piston. The standing wave produced is shown below. Its frequency is 60 Hz. The diagram is 1.8 m wide, end-to-end

A)(2) What is the wavelength?

B)(2) What is the propagation speed?

The frequency is adjusted so that the wave space contains 4 full waves.

C)What is the propagation speed?

D)What is the wavelength?

E)What is the frequency?

5. A student stands 1 m from a screen. Hydrogen light is diffracted through a grating that has 600 lines per mm. The student reports that a spectral line sits at the position _____ cm relative to the center of the screen. Solve for the wavelength of the photons in this spectral line.

6. A sound wave is created with frequency f0, wavelength 0, and speed v0. Answer each of the following correctly about changes to either f, , or v. Describe change in value through either multiplication or division by the dimensionless number n. n would be greater than 1. For example, a decrease in speed would be described as v = v0/n. As long as n > 1, this would accurately describes a decrease no matter what v0 and v are.

  1. The wave passes from a medium of low density to high density. It is a traveling wave, not a standing wave, in both media.
  1. v =
  2. f =
  3.  =
  1. The wave never changes media as it travels, but the membrane that causes the oscillation is pulled tighter to give it a greater elastic constant.
  1. v =
  2. f =
  3.  =
  1. The wave is set up as a standing wave in a column of fixed length. The wave being looked at is the one that fills the space with ¾ of a wave. The temperature of the air in the column increases. After the temperature changes, the wave being looked at is again the one that fills the space with ¾ of a wave.
  1. v =
  2. f =
  3.  =

7. The wavelengths of visible light are in a range closest to

A.the thickness of a sheet of paper.D. your height.

B.the diameter of your thumb.E. the length of a football field.

C.your belt size.

8.Which of the following statements concerning blue and red light is true?

A. Red light has a longer wavelength and higher frequency than blue light.

B. Red light has a shorter wavelength and higher frequency than blue light.

C. Red light has a longer wavelength and lower frequency than blue light.

D. Red light has a shorter wavelength and lower frequency than blue light.

E. none of these

9. In an experiment sources of white light, red light, and blue light are viewed first through a single narrow slit, then the viewing is repeated using two narrow parallel slits. Which of the following are observed in BOTH patterns?

i.When white light is viewed, colors were seen in the pattern.

ii.All nodal (or fringe) lines are equally spaced.

iii.The nodal line spacing is greater in the red pattern than in the blue pattern.

A. iii only B. i, ii, & iii C. ii & iii only D. i & ii only E. i & iii only

10. White light is viewed through a diffraction grating and is dispersed into a color spectrum. The color seen in the spectrum farthest from the light source is

A. red B. orange C. yellow D. green E. violet

11. For an experiment, a student can choose between two diffraction gratings; one has 5000 lines/cm and the other 7500 lines/cm. If a monochromatic light source is to be viewed through the grating, which one of the following will be true?

A.When viewed through the 5000 line/cm grating, the light will be seen farthest

from the center line.

B.When viewed through the 7500 line/cm grating, the light will be seen farthest

from the center line.

C.The light will be seen at the same position through either grating.

12. Two light waves from different sources arrive at the same point at the same time and their amplitudes add algebraically according to the principle of superposition. This is called

A.Dispersion B. Refraction C. Diffraction D. Interference E. Polarization

13.When light passes from air into water, what happens to the speed and the wavelength of light as it crosses the boundary in going from air into water?

SpeedWavelength

a. Increases Remains the same

b. Remains the sameDecreases

c. Remains the same Remains the same

d. Decreases Increases

e. DecreasesDecreases

14. One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown above. and is reflected at the wall. Properties of the reflected pulse include which of the following?

I. It has a greater speed than that of the incident pulse.

II. It has a greater amplitude than that of the incident pulse.

III. It is on the opposite side of the string from the incident pulse.

a. none b. III only c. I and II only d. II and III only e. I, II, and III

15. A light ray passes through substances 1, 2, and 3, as shown above. The indices of refraction for these three substances are n1, n2, and n3, respectively. Ray segments in 1 and in 3 are parallel. From the directions of the ray, one can conclude that

a. n3 must be the same as n1b. n2 must be less than n1

c. n2 must be less than n3d. n1 must be equal to 1.00

e. all three indices must be the same

16. A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown above, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be greatest?

a. A b. B c. C d. D e. It will be the same at all four points.

17. Two wave pulses. each of wavelength i., are traveling toward each other along a rope as shown. When both pulses are in the region between points X and Y. which are a distance i. apart. the shape of the rope is which choice?

18. Two sinusoidal functions of time are combined to obtain the result shown in the figure above. Which of the following can best be explained by using this figure?

(A) Beats (B) Doppler effect (C) Diffraction (D) Polarization (E) Simple harmonic motion

19. An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring. also with period T. If the masses of both objects are doubled. what are the new values for the Periods?

PendulumMass on Spring

(A)

(B) T

(C) T T

(D) T

(E)

20. Plane sound waves of wavelength 0.12 m are incident on two narrow slits in a box with nonreflecting walls, as shown above. At a distance of 5.0 m from the center of the slits, a firstorder maximum occurs at point P, which is 3.0 m from the central maximum. The distance between the slits is most nearly

a. 0.07 m b. 0.09 m c. 0.16 m d. 0.20 m e. 0.24 m

21. You will make standing waves by oscillating an elastic string that is anchored at one end and has a mass hanging from the opposite end. The end-to-end distance of the string is 1 meter.

  1. (2) At some frequency, the standing wave produced is exactly two wavelengths. Sketch this standing wave.
  2. (2) The wave’s speed is determined by v = (T/M)1/2 where the tension T is 2 Newtons and mass density M is 4 x 10-3 kg/m. Use this information to find the speed of the wave that you sketched in A.
  3. (1) What is the wavelength of the wave you sketched in part A?
  4. (2) What is the frequency of the wave you sketched in part A?
  5. You change the frequency and produce a new wave that is now exactly 3 full wavelengths between the endpoints of the string. For this wave:
  1. (2) What is the wave speed?
  2. (1) What is the wavelength?
  3. (2) What is the frequency setting

Key:

General Waves, INTERFERENCE AND DIFFRACTION OF LIGHT

On Planet X, two tuning forks are side-by-side making sound. One is pitched at 500 Hz with a wavelength of 2.5 m. The other is pitched at 2500 Hz. Call the first one wave A and the second one wave B.

  1. Find the speed of wave A. 1250 m/s
  2. Find the speed of wave B. 1250 m/s

2.A yellowish-green color has a wavelength of 550 nm. Find the frequency that generated this color. f = c/ = (3 x 1017nm/s)(5.5 x 102nm) = (3/5.5) x 1015 s-1

3. A source of light contains all possible categories of electromagnetic waves, not just the visible category. In an experiment, astronauts in space shine this light vertically onto a surface that is covered with a layer of air that is precisely 660 nm thick. The light travels from the vacuum of space through the layer of air and reflects off of the solid surface that is behind the air layer. When the light originally travels from vacuum to the air layer, it partially reflects off the initial surface of the air layer and it partially passes through. The part that makes it through travels to the solid surface where there is full reflection. Both the reflections off of the air layer and off of the solid surface invert the wave.

Note: The index of refraction of air is very close to 1, so light wavelengths in air are about the same as they are in vacuum.

Any questions below that ask about reflected light are referring to what is observed in the sum total of all the reflected light that comes off of this air/surface complex.

Path shift question. Students were told to study the simple wave addition ideas that underlie the origin of the interference equations like dsin = m. Those path shift ideas are the heart of this problem, and this problem has nothing to do with dsin = m.

  1. Calculate the longest wavelength that can exist in the total of the reflected light.

2d is the difference of wave travel distance when comparing the reflection off the top surface and the reflection off of the undersurface. Either 1 wavelength can fit in this or 2 or more, but no less than one.

2d =  = 2(660 nm) = 1320 nm = answer by common sense

(Some versions had 600 nm wavelength and their answer was 1200 nm.)

Formal proof of the method above:

2d = n with integer n or else interference is not constructive.

2d/ = n and n > 1 by definition of integers

2d/> 1 →  < d/2 d/2 is the longest the wavelength can be.

  1. Why is the proof method good? Because it allows all other solutions to the rest of this question. Let n be higher integers, AKA more waves fitting in the 2d space, then  decreases in controlled predictable ways.

2d = 2  = 660 nm etc…

  1. Calculate the third longest wavelength that can exist in the total of the reflected light. 440 nm
  2. Come up with a value of an air layer thickness that would only allow ONE possible visible color in the total reflected light.

The given d = 660 nm allows 660 nm and 440 nm to exist as the answers to A and B. Both of those are visible. They are red and violet. d is proportional to , so either increase d a bit to put the answer to B above 700 nm or decrease d a bit to put the answer to C below 440 nm.

d = 750 nm would do it. It would make the answer to B 750 nm (IR) and the answer to C 500 nm (visible). The answer to A would be 1500 nm (IR) and the fourth possible mode would be at 330 nm (UV).

YOU do the exercise of finding a d that would make the answer to B visible but the answer to C and everything shorter than that ultraviolet.

When the College Board says “know the spectrum” they don’t mean superficial memorization. They mean underlying physical meaning and application.

  1. Excluding any of the answers you gave to A, B, or C, what other possible categories of the EM spectrum could exist in the total reflected light? Anything shorter than the previous answers: That’s UV, X-Ray, Gamma. This should be clear from the underlying concepts of parts A, B, C, and D and YOUR memorization of what is long and short in the whole spectrum. Applications.

4. Suppose a standing wave generator produces waves in the space between a piston and a rigid boundary that is located 1.8 m away from the piston. The standing wave produced is shown below. Its frequency is 60 Hz. The diagram is 1.8 m wide, end-to-end

  1. (2) What is the wavelength?1.2 m
  2. (2) What is the propagation speed? (1.2 m)(60 s-1) = (12)(6) ms-1 = 72 m/s no calculator

The frequency is adjusted so that the wave space contains 4 full waves.

  1. What is the propagation speed? 72 m/s concepts only, no math
  2. What is the wavelength? 0.45 m
  3. What is the frequency? f = v/ = (72 ms-1)/(0.45 m) = (144/0.9) s-1 = (1440/9) Hz = 160 Hz

5. A student stands 1 m from a screen. Hydrogen light is diffracted through a grating that has 600 lines per mm. The student reports that a spectral line sits at the position 28cm relative to the center of the screen. Solve for the wavelength of the photons in this spectral line.

(599 mm-1)-1sin[Tan-1(0.28)] = 1 →  = 450 nm

6. A. v = nv0, f = f0, λ = λ0

B. v = v0, f = nf0, λ = (λ0)/n

C. v = nv0, f = nf0, λ = λ0 (to make this happen, a different tuning force had to oscillate)

7. A

8. C

9. E

10. A

11. B

12. D

13. E

14. B

15. A

16. C

17. B

18. A

19. B

20. D

21. C. 0.5 m D. 44.7 Hz E. 22.4 m/s, 0.33 m, 67.8 Hz