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Physics 7C SS1, Lecture 5: Wave and Ray Models

Standing waves

Reflection/Refraction

Optics

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Agenda Determine content students want lecture

about Discuss any review material about

interference (including beats and standing waves)

Develop any current material about the ray model (reflection and refraction)

Introduce any new material about the ray model (optics)

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What should lecture cover?(1st choice)

Review of aspects of the wave model

1) Multiple-slit interference

2) Beats

3) Standing Waves

Move forward with the ray model

4) Reflection and refraction

5) Next material: lenses

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What should lecture cover?(2nd choice)

Review of aspects of the wave modeln Multiple-slit interference

1) Beats

2) Standing Waves

Move forward with the ray model

4) Reflection and refraction

5) Next material: lenses

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Interference Fundamentals = -4, -2, 0, +2… is constructive = -3, -, +… is destructive =anything else…is partial

2π 2π Unit circle

Wave 1

Wave 2

Difference€

t

T

€

x

λ

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Interference for differing frequencies: Beats

1 2 3 4 5

What type of interference occurs at each point?

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Interference for differing frequencies: Beats

1 2 3 4 5

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Interference for differing frequencies: Beats

1 2 3 4 5

The carrier frequency

The beat frequency

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Standing Waves Fundamental

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Standing Waves 2nd Harmonic

3rd Harmonic

N = “node”A = “antinode”

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Standing Waves 2nd Harmonic

3rd Harmonic

• What type of interference occurs at an antinode?

a) Constructive

b) Destructive

c) Time-dependentd) Depends which

antinode

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Testing Standing Waves When the wave looks like this:

the frequency is 45Hz. What is the lowest possible frequency?

a) 9 Hz

b) 12.5 Hz

c) 15 Hz

d) 30 Hz

e) 135 Hz

f) Other

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Testing Standing Waves When the wave looks like this:

the frequency is 45 Hz. What is the highest possible frequency?

a) 9 Hz

b) 12.5 Hz

c) 15 Hz

d) 30 Hz

e) 135 Hz

f) Other

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Testing Standing Waves The figure below is for node-node waves. Draw the same

harmonic for antinode-node waves.

If this frequency is 45 Hz. What is the lowest possible frequency?(enter a numeric response rounded to the nearest whole number, no

decimal places)

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Testing Standing Waves The figure below is for node-node waves. Draw the same harmonic for

antinode-node waves.

If this frequency is 45 Hz. What is the lowest possible frequency?(enter a numeric response rounded to the nearest whole number, no

decimal places)

a) 9 Hz

b) 12.5 Hz

c) 15 Hz

d) 30 Hz

e) 135 Hz

f) Other

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Wavefronts and Rays A wavefront represent

points of equal phase (e.g. the crest of the wave).

The ray shows the direction in which the wavefront is moving. Rays are

perpendicular to wavefronts.

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From spherical to planar wavefronts

Planar wave front Spherical wave front

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Identify the representation:1 2

(a) Both wavefront(b) Both ray(c) 1 is wavefront, 2 is ray(d) 1 is ray, 2 is wavefront

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What (typically) happens next?

1 2

(a) There is a reflected wave

(b) There is a transmitted wave

(c) Both reflected and transmitted waves

(d) Neither reflected nor transmitted waves

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Transmitted Ray: Drive a car from a well-paved road into rough

grass. Which way will it go?

(a) (b) (c)

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Transmitted Ray: Transmitted ray is bent, or “refracted”

Angle of Incidence

Angle of Refraction

Law of Refraction or “Snell’s Law:”

n1sin1=n2sin2

n : “index or refraction” speed of light in vacuum speed of light in material

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Reflected Ray Throw a ball at a wall, view from above.

Which is the correct path, assuming a perfectly elastic collision?

(a) (b) (c) (d)Depends

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Reflected Ray

Angle of Incidence

Angle of Reflection

NormalLine

Law of Reflection:

i=r

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Reflected Wavefronts

Angle of Incidence

Angle of Reflection

NormalLine

Law of Reflection:

i=r

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Observe the Water Compass

In which medium does light travel faster?

a) Air

b) Water

c) Same in both

What happens if the angle in the water gets increasingly large?

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Observe on the Optics Board What are you seeing?

Reflection Refraction Total Internal Reflection Convergence Divergence

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Light at an Interface (Activity 8.6.3 & FNT 1)

Incoming Ray

Plastic prismn = 1.5

On entering the prism (first boundary), which way will the light bend?

a) Up b) Down c) No bend

Airn = 1

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Light at an Interface

Incoming Ray

Plastic prismn = 1.5

Which Ray?(a)

(b)

(c)

Airn = 1

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Parallel rays are uncommon…how do lenses work on regular objects?

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What do we see?

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Every part of the tree reflects light, scattering it all directions.

A ray diagram is used to simplify this picture.