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Physics 1C

Physics 1C. Lecture 24A. There are distinct forms of EM waves at different frequencies (and wavelengths). Recall that the wave speed is given by: v wave = c = l f . Wavelengths for visible light range between 400nm (violet) and 700nm (red).

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Physics 1C

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  1. Physics 1C • Lecture 24A

  2. There are distinct forms of EM waves at different frequencies (and wavelengths). • Recall that the wave speed is given by: vwave = c = lf. • Wavelengths for visible light range between 400nm (violet) and 700nm (red). • There is no sharp division between one kind of EM wave and the next. • For example, you can have an X-ray and a Gamma Ray with the exact same wavelength. Spectrum of EM Waves

  3. Note the overlap between types of waves (such as UV and X-rays). • All EM waves have the same speed in a vacuum, what distinguishes the types are their frequencies or wavelengths. • Note that the visible section is a quite small portion of the spectrum. EM Spectrum

  4. Wavelengths of light can range from very long (radio, ~100km) to very short (gamma, ~1fm). • Frequencies have an equally long range of possible values: (gamma, ~1022Hz) to (radio, ~10Hz). • Visible light ranges from Red (700nm, 4x1014Hz) to Violet (400nm, 7x1014Hz) EM Spectrum

  5. Radio waves have a long wavelength (~100m) and thus are good for use as a communication tool (TV, AM, FM). • Microwaves are smaller (~1cm) and interfere easily with common things (μwave oven grates). • Infrared waves are produced by hot objects. EM Spectrum

  6. Visible light (~500nm) is detected by the human eye. We are most sensitive to yellow-green (560nm). • UV light (~100nm) that comes from the Sun is mostly absorbed by the Earth’s ozone layer. EM Spectrum

  7. X-rays (~0.1nm) are associated with fast electrons hitting off of a metal target (medical applications). • Gamma rays (~1fm) are emitted by radioactive nuclei. They can cause serious damage to living tissue as they penetrate deeply into most matter. EM Spectrum

  8. Spherical Waves • A spherical wave propagates radially outward from the source (for instance, your cell phone). • The energy propagates equally in all directions. • The intensity is: • The average power is the same through any spherical surface centered on the source. • Intensity will decrease as r increases.

  9. Cell Phone Intensity • Example • A cell phone emits 0.60Watts of 1.9GHz radio waves. What are the amplitudes of the electric and magnetic fields at a distance of 10cm? • Answer • Assume the cell phone is a point source of electromagnetic waves (or r = 0).

  10. Answer • The intensity of the radio waves at 10cm is: Cell Phone Intensity • We want the maximum values (amplitudes) for the electric and magnetic fields.

  11. Answer • For magnetic field we can turn to: Cell Phone Intensity

  12. Concept Question • The amplitude of the oscillating electric field at your cell phone is 8μV/m when you are 10km from the broadcast antenna. What is the electric field amplitude when you are 20km from the antenna? • A) 8μV/m. • B) 4μV/m. • C) 2μV/m. • D) 1μV/m

  13. Doppler Effect for Light • Since light is an EM wave, if the source or the observer moves with respect to each other the frequency of the wave will be Doppler shifted. • But since the speed of light is so large it takes a large relative speed, u, between the observer and the source for there to be any noticeable effect on the observed frequency, fo. • For light the Doppler equation becomes: • where fs is the frequency emitted by the source and c is the speed of light.

  14. Doppler Effect for Light • As with the previous Doppler equation, you take the top sign (positive) if the observer and the source are moving toward each other. • You take the bottom sign (negative) if the observer and the source are moving away from each other. • Note that this equation is valid only when the relative speed, u, is much smaller than c. • Astronomers use the Doppler Effect for light to see if distant objects are moving toward or away from us.

  15. How do we know that the Universe is expanding ? • Chemical Elements have characteristic frequencies. (We’ll discuss this more later in the course) • We assume that chemical elements are the same, and thus have the same characteristic frequencies everywhere in the universe. • We observe the frequencies from distant stars to be “red-shifted”, i.e. at frequencies lower than expected. • fo < fs means distant stars are moving away from us.

  16. Polarization of Light • Light from the sun is produced by the vibrations of multitude of atoms located there. • Each atom produces a wave with its own orientation of the electric field. • All directions of the electric field vector are equally possible and are in a plane perpendicular to the direction of propagation. • This type of wave is known as an unpolarized wave.

  17. Polarization of Light • A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point. • It is possible to polarize an unpolarized beam. • The most common technique for polarizing light is called polarization by selective absorption.

  18. Polarization of Light • In this technique, you use a material that transmits waves whose electric field vectors in that plane are parallel to a certain direction (transmission axis). • This material also absorbs waves whose electric field vectors are perpendicular to that direction. • This device is known as a polarizer. • The material is known as a Polaroid (1932).

  19. Polarization of Light • When you place a second polarizing sheet (called the analyzer) behind the polarizer, the intensity of the polarized beam that is transmitted will vary as: • where Io is the intensity of the polarized wave incident on the analyzer. • The angle θ is the angle between the transmission axes of the two polarizing sheets. • This is Malus’ Law.

  20. Polarization of Light • The intensity of the transmitted beam is the highest when the transmission axes are parallel. • The intensity is zero when the transmission axes are perpendicular to each other. • This would cause complete absorption. • In the middle, the axes are at 45º and less intensity occurs.

  21. The Nature of Light • An interesting question developed as to the nature of light: if light is indeed a wave then why can it travel from the Sun to Earth when there is no medium present? • The answer: Light is a particle (photon), particles do not require a medium. • But if light is a particle, then how can it bend around corners? • The answer: Light is a wave, waves that propagate outward can bend around an obstacle.

  22. The Nature of Light • But, if light is a wave how does that explain the photoelectric effect? • The answer: Light is a particle, only particles with high energy can eject the electrons. • But if light is a particle, then how does this explain the “standing wave” pattern I see with interference from double slits? • The answer: Light is a wave, waves will create bright/dark spots depending on path length difference.

  23. The Nature of Light • But how can light be both a particle and a wave? • We say that light can have both wavelike properties and particle-like properties. • This is called wave-particle duality. • In some experiments light acts as a wave and in others it acts as a particle. • Experimenters will find whatever they are testing for. • Nature prevents testing both qualities at the same time.

  24. The Nature of Light • We can identify light as being “particles” called photons. • Each photon has a particular energy which is quantified by its frequency. • h is called Planck’s constant and is: • Note how wave-particle duality is incorporated here, light interacts like a particle with other particles but its energy is for a given frequency like a wave.

  25. The Ray Approximation • From now on we will have to treat light as having both properties (wave and particle). • The ray approximation is used in geometrical optics to approximately represent beams of light. • We draw imaginary lines (known as light rays) along the direction of propagation of a single wave. • We can also represent this wave with wave fronts. • A wave front is a surface where the wave has the same phase and amplitude.

  26. The Ray Approximation • Light rays travel in straight lines in a given medium. • Light rays can cross. They do not interact with each other. Two rays can cross without either being affected in any way. • A light ray travels forever unless it interacts with matter. • It can interact with matter by either: reflection, refraction, scattering or absorption. • Light ray can also bend around sharp edges (diffraction) depending on the wavelength.

  27. Ray Approximation: Barrier • A wave meets a barrier with l<<d (d is the diameter of the opening). • The ray approximation assumes that the individual waves emerging from the opening continue to move in a straight line. • The wave meets a barrier with an opening size on the order of the wavelength: l~d. • The waves undergo diffraction and spread out from the opening in all directions.

  28. Ray Approximation: Barrier • The wave meets a barrier with an opening size much smaller than the wavelength: l >> d. • In this case, the opening can be approximated as a point source.

  29. Ray Model of Light • An object is a source of light rays. • Rays originate from every point on the object, and each point sends rays in all directions. • If the object is far away, the rays will appear parallel to the observer. • We make no distinction between self-luminous objects and reflective objects. • 5) The eye sees by focusing a diverging bundle of rays.

  30. The Nature of Light • The incident light ray will move in a straight line path as long as the medium does not change. • But, when it encounters a boundary with a second medium, (at least) part of this incident ray is reflected back into the first medium. • If the boundary is a smooth surface, the reflection is known as specular reflection. • This means all the reflected rays will be parallel to one another.

  31. The Nature of Light • If the boundary is a rough surface, the reflection is known as diffuse reflection. • This means that the reflected rays will travel in a variety of directions. • Diffuse reflection is how you can see most everyday objects. • Although diffuse reflection is more common, it is harder to mathematically model than specular reflection.

  32. Law of Reflection • We define a normal (perpendicular line to the surface) at the point where the incident ray hits strikes the surface. • The incident angle, θ1, is the angle that the incident ray makes with respect to the normal. • The reflected angle, θ’1, is the angle that the reflected ray makes with respect to the normal. • The angle of incidence is equal to the angle of reflection.

  33. For Next Time (FNT) • Continue Chapter 24 homework. • Start reading chapter 25.

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