1. Chapter 24 The Wave Nature of Light
Phy 2054
Lecture Notes

2. 24-01 Conditions for Interference
Wave Optics
Sections
Conditions for Interference
Young’s Double-Slit Experiment
Change of Phase Due to Reflection
Interference in Thin Films
Diffraction
Single-Slit Diffraction
The Diffraction Grating
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3. Conditions for Interference
For observable interference effects, sources must be
Waves must maintain
a constant phase
relationship
1. Coherent
2. Monochromatic
Waves must have
the same wavelength
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4. Two light sources are said to be coherent if they
Chapter 24: Wave Optics
Two light sources are said to be coherent if they
(A) are of the same frequency.
(B) are of the same frequency, and maintain a constant
phase difference.
(C) are of the same amplitude, and maintain a constant
(D) are of the same frequency and amplitude.
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5. Young’s Double-Slit Experiment
If light is a wave, interference effects will be seen, where one part of wavefront can interact with another part.
One way to study this is to do a double-slit experiment:
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6. Young’s Double-Slit Experiment
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7. Young’s Double-Slit Experiment
The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).
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8. Chapter 24: Wave Optics
What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits?
(A) refraction
(B) polarization
(C) dispersion
(D) interference
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9. Young’s Double-Slit Experiment
We can use geometry to find the conditions for constructive and destructive interference:
Bright
(constructive interference)
Dark
(destructive interference)
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10. Young’s Double-Slit Experiment
PS2 - PS1
= d sin(q) q S1 d q
Constructive Interference S2
Destructive Interference
screen
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11. Young’s Double-Slit Experiment
Bright q y L S1 d
Constructive Interference S2
screen
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12. Young’s Double-Slit Experiment
Dark q L y S1 d
Destructive Interference S2
screen
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13. (D) There is not enough information to determine.
Chapter 24: Wave Optics
In a Young's double slit experiment, if the separation between the slits decreases, what happens to the distance between the interference fringes?
(A) It decreases.
(B) It increases.
(C) It remains the same.
(D) There is not enough information to determine.
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14. (D) none of the given answers
Chapter 24: Wave Optics
At the first minima on either side of the central bright spot in a double-slit experiment, light from each opening arrives
(A) in phase.
(B) 90° out of phase.
(C) 180° out of phase.
(D) none of the given answers
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15. (A) each opening travels the same distance.
Chapter 24: Wave Optics
At the second maxima on either side of the central bright spot in a double-slit experiment, light from
(A) each opening travels the same distance.
(B) one opening travels twice as far as light from the other
opening.
(C) one opening travels one wavelength of light farther than
light from the other opening.
(D) one opening travels two wavelengths of light farther than
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16. Chapter 24: Wave Optics
What principle is responsible for light spreading as it passes through a narrow slit?
(A) refraction
(B) polarization
(C) diffraction
(D) interference
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17. Diffraction
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18. Single-Slit Diffraction
The resulting pattern of light and dark stripes is called a diffraction pattern.
This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would.
The minima of the single-slit diffraction pattern occur when
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19. Single-Slit Diffractionq d L
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20. (A) the same thing as without the fingers, but dimmer.
Chapter 24: Wave Optics
A person gazes at a very distant light source. If she now holds up two fingers, with a very small gap between them, and looks at the light source, she will see
(A) the same thing as without the fingers, but dimmer.
(B) a series of bright spots.
(C) a sequence of closely spaced bright lines.
(D) a hazy band of light varying from red at one side to
blue or violet at the other.
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21. Single-Slit Diffractiony d
A single slit of width 0.30 mm is
illuminated with 650 nm light. An
interference pattern is formed on a
screen 2.5 m away. Find the distance
from the first dark band to the central
bright band.
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22. Single-Slit Diffraction
A single slit of width 0.14 mm is illuminated by monochromatic
light and interference bands are observed on a screen 2.0 m away.
If the second dark band is 16 mm from the central bright band,
what is the wavelength of the light? L y q D
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23. The Diffraction Grating
A diffraction grating consists of a large number of equally spaced narrow slits or lines. A transmission grating has slits, while a reflection grating has lines that reflect light.
Two slits
Six slits
The more lines or slits there are, the narrower the peaks.
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24. (A) The grating with 3 slits produces the greater separation
Chapter 24: Wave Optics
Consider two diffraction gratings with the same slit separation, one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic light, make a statement concerning the separation between the orders.
(A) The grating with 3 slits produces the greater separation
between orders.
(B) The grating with 4 slits produces the greater separation
(C) Both gratings produce the same separation between orders.
(D) Both gratings produce the same separation between orders,
but the orders are better defined with the 4-slit grating.
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25. The Diffraction Grating
The maxima of the diffraction pattern are defined by
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26. The Diffraction Grating (Problem)
A 3500-line/cm grating produces a third-order fringe at
a 28.0o angle. What is the wavelength of light being used?
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27. The Diffraction Grating (Problem)
A diffraction grating has 6.0 x 105 lines/m. Find the angular spread in second-order spectrum between red light of wavelength 7.0 x 10-7 m and blue light of wavelength 4.5 x 10-7 m. B R qR qB Dq
m = 2
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28. The Diffraction Grating
The Spectrometer and Spectroscopy
A spectrometer makes accurate measurements of wavelengths using a diffraction grating or prism.
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29. The Diffraction Grating
The Spectrometer and Spectroscopy
The wavelength can be determined to high accuracy by measuring the angle at which the light is diffracted.
Atoms and molecules can be identified when they are in a thin gas through their characteristic emission lines.
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30. Change of Phase Due to Reflection
A reflected light wave undergoes a phase change of 180o.
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31. Change of Phase Due to Reflection
A reflected light wave undergoes no phase change.
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32. (A) a 90° phase change in the reflected beam.
Chapter 24: Wave Optics
When a beam of light, which is traveling in glass, strikes an air boundary, there is
(A) a 90° phase change in the reflected beam.
(B) a 180° phase change in the reflected beam.
(C) a 45° phase change in the reflected beam.
(D) no phase change in the reflected beam.
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33. Interference in Thin Films
Another way path lengths can differ, and waves interfere, is if they travel through different media.
If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference.
This can be seen in soap bubbles and oil slicks, for example.
glass
air
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34. Interference in Thin Films
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35. Interference in Thin Filmsa
The phase displacement of (b)
relative to (a) is b n t
There is darkness
There is brightness
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36. Interference in Thin Films (Problem)
A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are looking straight down from an airplane onto a region of the slick where its thickness is t = 460 nm.
Which wavelength of visible light is reflected the greatest?
n = 1.0 a b
air
kerosene
water
n’ = 1.2
n’’ = 1.3 t
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37. Interference in Thin Films
A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are a scuba-diver directly under the slick where its thickness is t = 460 nm.
Which wavelength of visible light is the transmitted intensity
the greatest?
n = 1.0 a b
air
kerosene
water
n’ = 1.2
n’’ = 1.3 t
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38. Interference in Thin Films
One can also create a thin film of air by creating a wedge-shaped gap between two pieces of glass.
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39. Interference in Thin FilmsB R I G H T B R I G H T D A R K D A R K D A R K
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40. Interference in Thin Films
Problem Solving: Interference
Interference occurs when two or more waves arrive simultaneously at the same point in space.
Constructive interference occurs when the waves are in phase.
Destructive interference occurs when the waves are out of phase.
An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.
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41. END