Optics Course (Phys 311)

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Optics Course (Phys 311)

Wave Optics

Electromagnetic Waves

Lecturer: Dr Zeina Hashim

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Phys 311

1. Sources of EM waves.

2. Maxwell’s Equations.

3. Electric Field and Magnetic Field wave equations.

4. The Speed of EM Waves.

5. Representation of EM Waves.

6. Energy and Poynting Vector of EM Waves.

7. Irradiance.

Wave Optics: EM Waves

Objectives covered in this lesson :

Lesson 1 of 1 Slide 1

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Some EM waves are radiated from atoms and nuclei:

X-rays , gamma rays , visible light

Some EM waves are generated by EM-wave generators:

Radio waves Phys

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Sources of EM Waves :

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The generation of Radio waves:

(just to read) Phys

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We previously defined a wave as a disturbance of a medium. How come an EM wave can exist in vacuum and travel from the sun to Earth ?

This was explained when Maxwell put forward his famous EM theory of light:

From his 4 equations  he derived the wave equation.

 it predicted the existence of EM waves.

From the wave equation  he could calculate the speed of EM waves in free space:

His theoretical value of the speed was similar to the experimental value of speed of light.

 “Light must be an electromagnetic wave”

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According to Maxwell:

Phys 311

EM waves consist of changing E field that generates a changing B field, facilitating the propagation of the EM

wave even in the absence of matter.

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Phys 311

Maxwell’s Equations :

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Phys 311

The above equations may also be written in differential forms as:

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5. The fields always vary sinosoidally, with the same speed and in-phase (in step) with each other.

Phys 311

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Q: What are the directions of these waves?

Q: What are Em and Bm ? Q: What is omega?

Q: What is k ? Phys

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Magnetic and Electric Field Wave Equations :

In the positive x-direction.

They are the amplitudes of the fields.

The angular frequency.

The propagation number.

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Each field forms its own wave, each is a wave component of the EM wave:

Electric wave component

Magnetic wave component

Each of the components satisfies the one-dimensional differential wave equation.

However, these two wave components cannot exist independently.

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From the wave equations:

EM waves travel with the speed of light (c). So, use c instead of v in the mathematical formula:

The speed and amplitudes (also speed and magnitudes) of the electric and magnetic fields are related by:

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The Speed of EM Waves :

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Representation of EM Waves :

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Energy of EM Waves :

Electric and magnetic fields

store energy.

Energy can also be carried by the EM

waves which consist of both

fields.

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Poynting Vector of EM Waves :

the rate of change of energy per unit area, denoted with the symbol S, is the pointing vector (after the British physicist John Poynting).

The SI unit of S is W/m².

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Wave Optics: Wave Motion

Irradiance (Intensity) :

Irradiance : is the intensity of the wave, I, defined as the time average of S.

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For a harmonic wave:

Substitute in I : Phys

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Q1 :

Q2 : Phys

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Homework :

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Q3 :

Q4 : Phys

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Homework :

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1. Sources of EM waves.

2. Maxwell’s Equations.

3. Electric Field and Magnetic Field wave equations.

4. The Speed of EM Waves.

5. Representation of EM Waves.

6. Energy and Poynting Vector of EM Waves.

7. Irradiance.

Phys 311

Lesson 1 of 1 Slide 25 (last)

Summary:

Any Questions?

Next lesson will be:

Midterm Exam ! Wave Optics: EM Waves