Interference II Pt I

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?

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

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

The speakers are ______ wavelength(s) apart so the crests are ______. 
What does the superposition look like? and what is Δd?

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)

The individual waves are ____ _____ and therefore are indistinguishable. They also exhibit ________ interference (explain) 

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

The speakers are ____ wavelength apart so crests meet _______. The superposition is a wave with _____ amplitude. What is Δd?

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?

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)

In a Perfect destructive interference state the formula for:
ΔΦ 
ΔΦ₀ (for identical sources)
Δx (explain)

What are three ways of achieving destructive interference

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

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

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 

Case 2: λ ~ d
The waves spread out from the opening in ____ ______. The waves undergo _______
Label the diagram:

Case 3: λ>>d
The diffraction is so great that the opening can be approximated as a ______ ______. Light _____ ____ behind the slit

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?

What are the Two Big Rules for Waves

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

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 λ_medium

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

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:

A plane wave is incident on the _______ _____
Waves _____ ____ behind each slit
Constructive interference occurs when r₁ and r₂ differ by a _____ ______ of wavelengths
Destructive interference occurs when r₁ and r₂ differ by a _____ _____ of wavelengths plus _____ a wavelength
The bright fringes are labeled by the integer m, starting at the ______ ______

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