Ph272- General Physics II (Electricity and Magnetsism)

Lecture 25-26: Ch. 33 - Speed of light, Reflection, Refraction

Key Topics

Overview

• Visible light is an E & M wave and it is important to humans because our eyes are sensitive to this part of the spectrum
• We will discuss reflection and refraction. These phenomena are true for all kinds of waves, not just E&M waves. You will see that refraction occurs whenever the wave speed varies from one medium to another. Rainbow colors appear because the wave speed depends on the frequency of the wave.

Speed of Light

• Speed of light in vacuum: The E&M wave speed in vacuum is the same for all frequencies; c=1/sqrt(mu* epsilon) = 3x10**8 m/s.
• Speed of light in a medium: In a medium, the values for mu and epsilon could be different from those in vacuum. Furthermore, mu and epsilon depends on the frequency of the wave. Hence the E&M wave speed in a medium is different from that in the vacuum and the wave speed depends on frequency of the wave. Generally, the E&M wave speed (v) in a medium is lower than that in vaccuum.

We write: v = c/n . This equation defines n, n is called the index of refraction.

Since v depends on frequency, so is n.

See Table 30-1, P. 991 for n for various materials for the yellow light.

See Fig. 30-22 for variation of n for different wavelength (related to frequency)

Reflection

• When an E&M wave hits a boundary of two media, a reflected wave is generated (and a transmitted wave)
• Law of reflection: angle of incidence = angle of reflection
• Reflected intensity: Generally the reflected intensity depends on the orientations of the E-field and B-field of the E&M wave relative to the reflecting surface. However, for normal (incidence angle of incidence=0), the reflected intensity is given by a simple formula, Eq. 30-3, P. 982.

Note: Try to understand this formula.

If n1=n2 (i.e. the two medium are the same => there is no boundary) what should the reflected intensity be?

If n1 and n2 are very different, what would the reflected intensity be?

Refraction

• When a wave enter from one medium into another at an oblique angle (not normal incidence), the transmitted wave will be refracted (bent).
• Refraction is due to change in wave speed from medium 1 to medium 2.
• (Use the lawn mover analog: Discussion in class).
• Law of refraction: I prefer Eq. 30-5 (P.986) because it shows that refraction caused by change in wave speed. However, Eq. 30-6 is commonly used (they are the same equation).
• Total internal reflection: Occurs only when light enters from a slower medium (larger n) into a faster medium (smaller n). At a certain angle of incidence, there is no refracted wave. See Eq. 30-7 and Fig. 30-17, P. 987. Do example 30-6 (calculate critcal angle for total internal reflection.

Optical fibers utilize the total internal reflection phenomenon to keep the light intensity within the fiber.

Modern day fiber actually has concentric layers of materials when varying index of refraction.

• Dispersion: Due to index of refraction depends on frequency (wavelength).
• Rainbow: Refraction by raindrop. It turns out that at 42 degree from horizon, the refracted ray is the strongest (the sun is behind you and on the horizon, that is why you see rainbow in the morning or late afteroon), see Fig. 30-24 and 30-25, P. 992.

Polarization

• Polarization of an E&M wave is defined to be the direction of the E-field.
• If the E-field oscillates along a line, we called this wave linearly polarized (We don't have to consider the B-field because the B-field direction can be determined from the E-field and the propagation direction (E x B point to the propagation direction).
• Most sources are non-coherent, that is, the E&M waves generated by different atoms have their E-field pointing in different directions. The net result is an unpolarized light.
• An unpolarized light can turn into linearly polarized by a polarizer.
• Understand what happens to the transmitted intensity when more than one polarizer is placed in sequence.
• We will discuss qualitatively "polarization by scaterring" and "polarization by refection" in class (and demonstration of these effects).

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