Classical and Modern Optics - Home Exercise 1
1. An infinite rod lays on the z-axis, and carries the following current:
(
0 t≤0
I=
I0 t > 0
Find the induced electric and magnetic fields.
2. [Hecht 3.13] Prove that the irradiance of the harmonic EM-wave is given by
I=
1
E2
2cµ0 0
and then determine the average rate at which energy is transported per unit area by a plane
wave having an amplitude of 15.0 V /m.
3. [Hecht 3.31] The average magnitude of the Poynting vector for sunlight arriving at the top of
Earth’s atmosphere (1.5 × 1011 m from the Sun) is about 1.4kW m2 .
(a) Compute the average radiation pressure exerted on a metal reflector (a perfect reflector)
facing the Sun.
(b) Approximate the average radiation pressure at the surface of the Sun whose diameter is
1.4 × 109 m.
4. [Hecht 3.40] Given that the wavelength of a lightwave in vacuum is 540nm, what will it be in
water, where n = 1.33?
5. What are normal dispersion and anomalous dispersion? Explain why they are called this way,
and when each of them emerges.
6. Following the exercise we solved in class, find the dispersion relation, n(ω), for a gas with
multiple resonance frequencies, neglecting the damping term. Show that for ω ω0 B
n(λ) ≈ 1 + A 1 + 2
λ
and find A and B.
This equation is Augustin Louis Cauchy’s formula. Read about the meaning of A and B, and
explain it.
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