16.5 Interference in One Dimension
Two traveling waves can pass through each other without being ______ or ______. A consequence of the ________ principle.
What two factors do the amplitude of the resultant wave depend on?
- destroyed or altered
- superposition principle
- Interference: when two or more waves are superimposed on each other, and combine to form a single resultant wave
- Depends on:
- The amplitudes of the combining waves
- How these waves travel relative to each other
Assume the 2 waves are sinusoidal, have the same ______ and ______, and travel to the right along the x axis, state the formula for D1 and D2.
Φ10 and Φ20 are characteristics of the _____, not the ______
What do Φ1 and Φ2 represent
- same frequency and amplitude
- sources not the medium
- Φ1 and Φ2 are the phases of the waves
If crest meets crest, and trough meets trough, we say that the waves are ____ ____ with each other.
Φ1 = ___ or Φ1 = _______, where m is an integer.
Their amplitudes will _____, and we say the waves interfere ______.
The amplitude of the resultant pulse is _______ than either individual pulse
- in phase
- Φ1 = Φ2 or Φ1 = Φ2±2πm
- interfere constructively
- greater than
The speakers are ______ wavelength(s) apart so the crests are ______.
What does the superposition look like? and what is Δd?
- Superposition a wave with larger amplitude
When Φ1 = Φ2 or Φ1 = Φ2±2πm, where m = 0, 1, 2, 3,...
The amplitude of the resultant wave is ____. The crests of one wave ______ with the crests of the other wave.
The waves are in _____ everywhere.
The waves interfere ________ (state the formula for ΔΦ)
- in phase
- ΔΦ = 2πm
The individual waves are ____ _____ and therefore are indistinguishable. They also exhibit ________ interference (explain)
- in phase
- constructive interference (amplitudes add)
When can we say waves are out of phase (180° or π radian out of phase) with each other?
Their amplitudes ______ and we say the waves interfere ______. The amplitude of the resultant pulse is ______ than either individual pulse
- 180° or π radian out of phase: If the crest of one wave coincides with the trough of the other (and vice versa)
- interfere destructively
- less than
The speakers are ____ wavelength apart so crests meet _______. The superposition is a wave with _____ amplitude. What is Δd?
- 1/2 wavelength apart
- zero amplitude
- Δd is the path-length difference
The amplitude of the resultant wave is ____. Crests of one wave coincide with ______ of the other wave. The waves interfere ________ so the waves ______. The individual waves are ____ ____ ____ ____. Label the diagram and what is the formula for ΔΦ and its m series?
- 180° out of phase
- m = 0, 1, 2, 3,...
Restate the formula for Φ1 and Φ2. Then state the formula for phase difference (3) and specify the meaning of the components of its final formula
For maximum constructive interference:
State the formula for ΔΦ (2) rad where m = 0, 1, 2, 3,...
For identical sources, ie. ΔΦ0 = ___, when does maximum constructive interference occur? (explain)
- ΔΦ0 = 0
- when Δx = mλ (when the path-length difference is an integer number of wavelength)
In a Perfect destructive interference state the formula for:
ΔΦ0 (for identical sources)
What are three ways of achieving destructive interference
- (Path difference)/(wavelength) = Δx/λ
- whole number results (0, ±1, ±2, ±3...)are constructive interference and half numbers are destructive interference
- a) (6-2)/4 = 1 aka constructive
- b) (5-3)/4 = 1/2 aka destructive
- c) (4-4)/4 = 0 aka constructive
- d) (3-5)/4 = -1/2 aka destructive
- e) (2-6)/4 = -1 aka constructive
What are the 3 Models of Light?
Geometric optics involves the study of the ______ ____ _____. The _____ ______ is used to represent beams of light.
Define a ray and state 2 of its uses
- propagation of light
- ray approximation
- Ray: a straight line drawn along the direction of propagation of a single wave
- 1) it shows the path of the wave as it travels through space
- 2) It is a simplification model
The rays are straight lines _______ to the wave fronts. With the ray approximation, we assume that a wave moving through a medium travels in a ______ ______ in the directions of its rays. Label the diagram
- straight line
Case 1: λ<<d
In the Ray Model, in Geometric Optics, define:
The individual waves emerging from the opening continue to move in a _____ _____. Good for the study of mirrors, lenses, prisms, and associated optical instruments
Label the diagram
- λ: wavelength of the ray
- d: the diameter of the opening or barrier
- straight line
Case 2: λ ~ d
The waves spread out from the opening in ____ ______. The waves undergo _______
Label the diagram:
- all directions
Case 3: λ>>d
The diffraction is so great that the opening can be approximated as a ______ ______. Light _____ ____ behind the slit
- point source
- spreads out
Light wave travels with speed c in a vacuum, but they _____ _____ as they pass through transparent materials. The speed of light in a material is characterized by the material's ______ ____ ______ (__) (state the formula)
What changes for n in a vacuum vs in other media?
- slow down
- index of refraction (n)
What are the Two Big Rules for Waves
- The speed of a wave is determined by the type of wave and the characteristics of the medium, not by the frequency
- When a wave passes into another medium, its speed changes, but its frequency does not.
Referring back to rule #1
The speed of a wave is determined by the type of wave and the characteristics of the medium, not by the frequency.
Since v = ___ and the wave speed is NOT dependent on _______. Therefore, if frequency changes, it only affects the ________ (__), not v
- v = λf
- wavelength (λ)
Referring back to rule #2
When a wave passes into another medium, its speed changes, but its frequency does not.
Frequency of a wave is the ________ of the source. In different medium, the wave speed ______. Thus, the wave will undergo a different ________ in different medium
As light travels from one medium to another, its _______ remains constant. Since v varies from one medium to another, this implies _______ varies.
State the formula for λmedium
- λmedium = λvacuum/n
This is a transparent material in which light travels ______, at speed v = ____.
The wavelength inside the material ________, but the frequency does not
- v = c/n
Define Monochromatic, coherent and incoherent
The superposition principle allows us to add up ______ ______ by adding their ___ and ___ fields
Define Constructive and Destructive
For light to display interference, it must be ________
In constructive interference, the amplitude of the resultant wave is ______ than that of either individual wave. In destructive interference, the amplitude of the resultant wave is _____ than that of either individual wave
To observe interference in light waves, what two conditions must be met:
- The sources should be monochromatic
- The sources must be coherent
A plane wave is incident on the _______ _____
Waves _____ ____ behind each slit
Constructive interference occurs when r1
differ by a _____ ______ of wavelengths
Destructive interference occurs when r1
differ by a _____ _____ of wavelengths plus _____ a wavelength
The bright fringes are labeled by the integer m, starting at the ______ ______
- double slit
- spread out
- whole number
- whole number
- central maximum
Most cases, d << L → θ is ______
Thus, we can use small angle approximation:
sin θ ~ _____ ~ _____
State the formula for
Path difference Δr (2)