Questions: Electromagnetic Waves in Dielectric Media

Question 1

A glass prism separates white light into a spectrum of colors. Which explanation correctly identifies the physical mechanism?

• A. The index of refraction depends on frequency, so different colors bend by different amounts at each glass-air interface
• B. The prism absorbs high-frequency light more than low-frequency light, transmitting only the lower-frequency colors
• C. Different colors have different wavelengths in vacuum, and the prism physically sorts them by wavelength at the surface
• D. Different colors travel at the same speed inside glass but exit at different angles due to their different vacuum wavelengths

Answer: (A)

The mechanism is dispersion: n(ω) depends on frequency because bound charges in the glass are driven oscillators that respond differently at different driving frequencies. Higher-frequency light (blue) has a slightly higher n than lower-frequency light (red), so it travels slower and bends more at each interface. Options C and D confuse the fact of different wavelengths with the mechanism — it is the frequency-dependent refractive index that causes different deflection angles, not wavelength sorting per se. The driven-oscillator model of bound charges is the microscopic origin of dispersion.

Question 2

An electromagnetic wave propagating into a good electrical conductor like copper behaves as follows at radio frequencies:

• A. It passes through largely unchanged but at a slower speed due to the high permittivity of metals
• B. It reflects perfectly at the surface with absolutely zero penetration into the conductor
• C. Its amplitude decays exponentially with depth, penetrating only a characteristic skin depth before being effectively attenuated
• D. It accelerates inside the conductor because free electrons assist wave propagation

Answer: (C)

In a conductor, free charges respond to the wave and dissipate energy. The permittivity becomes complex, giving an imaginary component to the index of refraction. The imaginary part causes exponential amplitude decay exp(−z/δ), where δ is the skin depth. Option B (perfect reflection) is the common misconception — there is always some penetration, but for good conductors at RF frequencies the skin depth is very small (micrometers), making reflection nearly total but not exactly perfect. This is why RF signals are shielded by conductive enclosures.

Question 3

In vacuum, the dispersion relation for electromagnetic waves is linear (ω = ck), meaning all frequencies of light travel at exactly the same speed regardless of wavelength.

• T. True
• F. False

Answer: True

In vacuum, Maxwell's equations yield ω = ck, where the phase velocity ω/k = c is identical for all frequencies. This non-dispersive propagation means a pulse maintains its shape as it travels, because all frequency components move together. This linearity is broken inside any material medium: the driven-oscillator response of bound (or free) charges makes ε_r frequency-dependent, bending the dispersion relation so that ω/k varies with frequency and different colors travel at different speeds.

Question 4

Light slows down inside a glass window because it is repeatedly absorbed and re-emitted by glass atoms, and the time spent in this absorption process accounts for the reduced phase velocity.

• T. True
• F. False

Answer: False

This is a common but incorrect folk explanation. The correct account is that bound charges in the dielectric are driven oscillators responding to the electromagnetic wave's electric field. Their polarization response modifies Maxwell's equations — replacing ε₀ with ε = ε_r ε₀ — which changes the wave's phase velocity to v_p = c/n without any absorption-and-re-emission mechanism. The electromagnetic wave is a coherent field solution that propagates continuously through the medium; it is not a stream of photons individually captured and released by separate atoms.

Question 5

Why does a glass prism separate colors, and what is the underlying physical reason that different frequencies of light travel at different speeds inside glass?

Model answer: Different colors correspond to different frequencies. Inside glass, the index of refraction n depends on frequency because the bound electrons in glass behave as driven oscillators: they respond differently to different driving frequencies, especially near their natural resonances. This frequency-dependent response modifies the permittivity ε_r(ω), which changes the phase velocity v_p = c/n(ω) for each frequency. Blue light (higher ω) has a higher n and bends more at the glass-air interface; red light (lower ω) bends less. The spatial separation of colors at the exit face makes this dispersion visible as a spectrum.

Dispersion originates from the resonant response of bound charges. Far from resonances, n increases gently with frequency for most transparent materials — so-called 'normal dispersion.' Near a resonance the behavior becomes anomalous. The prism converts a continuous spread of phase velocities into a spatial spread of directions, making the frequency dependence of n directly observable.