
16.5 Interference in One Dimension
Two traveling waves can pass through each other without being ______ or ______. A consequence of the ________ principle.
Define Interference
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.
Φ_{10} and Φ_{20} are characteristics of the _____, not the ______
What do Φ_{1} and Φ_{2} represent
 same frequency and amplitude

 sources not the medium
 Φ_{1} and Φ_{2} are the phases of the waves

If crest meets crest, and trough meets trough, we say that the waves are ____ ____ with each other.
Φ_{1} = ___ or Φ_{1} = _______, 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
 Φ_{1} = Φ_{2} or Φ1 = Φ_{2}±2πm
 add
 interfere constructively
 greater than

The speakers are ______ wavelength(s) apart so the crests are ______.
What does the superposition look like? and what is Δd?
 one
 aligned
 Superposition a wave with larger amplitude

When Φ_{1} = Φ_{2} or Φ_{1} = Φ_{2}±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)
 2a
 coincides
 in phase
 constructively
 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)
 subtract
 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
 troughs
 zero amplitude
 Δd is the pathlength 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?
 0
 troughs
 destructively
 cancel
 180° out of phase
 m = 0, 1, 2, 3,...

Restate the formula for Φ_{1} and Φ_{2}. 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. ΔΦ_{0} = ___, when does maximum constructive interference occur? (explain)
 ΔΦ_{0} = 0
 when Δx = mλ (when the pathlength difference is an integer number of wavelength)

In a Perfect destructive interference state the formula for:
ΔΦ
ΔΦ_{0 }(for identical sources)
Δx (explain)

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) (62)/4 = 1 aka constructive
 b) (53)/4 = 1/2 aka destructive
 c) (44)/4 = 0 aka constructive
 d) (35)/4 = 1/2 aka destructive
 e) (26)/4 = 1 aka constructive



What are the 3 Models of Light?
(define each)

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
 perpendicular
 straight line

Case 1: λ<<d
In the Ray Model, in Geometric Optics, define:
λ
d
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
 diffraction

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
 frequency
 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
 frequency
 changes
 wavelength

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 λ_{medium}
 frequency
 wavelength
 λ_{medium} = λ_{vacuum}/n

This is a transparent material in which light travels ______, at speed v = ____.
The wavelength inside the material ________, but the frequency does not
 slower
 v = c/n
 decreases

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 r _{1} and r _{2} differ by a _____ ______ of wavelengths
Destructive interference occurs when r _{1} and r _{2} 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
 half
 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)
tan θ
y
 small

