Chapter #25 Solutions - Introduction to Optics - Leno M Pedrotti, Leno S Pedrotti, Frank L Pedrotti - 3rd Edition

 

1. In general, the “electrical constant” K, the dielectric constant, is related to the refractive index by K = n2a. Show that if KR and KI are the real and imaginary parts of the dielectric constant, then ...and ...b. Calculate nR and nI for a dielectric, in terms of KI, at frequencies high enough such that KI = KR. Get solution

2. Show that in a nearly transparent medium, the absorption coefficient is related to the conductivity and refractive index by ... Get solution

3. Calculate and/or plot real and imaginary parts of the refractive index for a dielectric given the frictional parameter γ, the resonant frequency ω0, and the dipole density N. Check your calculations against Figure 25-2. Get solution

4. Assume that aluminum has one free electron per atom and a static conductivity given by 3.54 × 107/Ω-m. Determine (a) the frictional constant γ, (b) the plasma frequency ωp, (c) the real and imaginary parts of the refractive index at 550 nm. Get solution

5. Show that Eq. (25-58) for the skin depth at low frequency is an adequate approximation when ω ≪ γ and ω ≪ σ/ε0. Get solution

6. Calculate the skin depth in copper for radiation of (a) 60 Hz and (b) 3 m. First ensure that the approximations of problem 1 are satisfied. (Handbook data for copper: σ = 5.76 × 107/Ω-m.)Problem 1Show that Eq. (25-58) for the skin depth at low frequency is an adequate approximation when ω ≪ γ and ω ≪ σ/ε0. Get solution

7. Compare the skin depth of (a) aluminum, with conductivity of 3.54 × 107/Ω-m and (b) seawater, with conductivity of 4.3/Ω-m, for radio waves of 60 kHz. Get solution

8. Calculate the skin depth of a solid silver waveguide component for 10-cm microwaves. Silver has a conductivity of 3 × 107/Ω-m. Explain why a more economical silver-plated brass component will work as well. Get solution

9. The energy density of red light of wavelength 660 nm is reduced to one-quarter of its original value by passage through 342 cm of seawater.a. What is the absorption coefficient of seawater for red light of this wavelength?b. At what depth is red light reduced to 1 % of its original energy density? Get solution

10. Calculate and/or plot the real and imaginary parts of the refractive index for a metal, given the frictional parameter and the plasma frequency. Check your results against Figure 1.Figure 1Angular frequency dependence of the refractive index nR and the extinction coefficient nI for copper. Values assumed are ωp = 1.63 × 1016 s−1 and γ = 4.1 × 1013 s−1. The crossover point of the curves coincides with the plasma frequency.... Get solution

11. Determine the theoretical content of the constants A, B, and C used to express the Cauchy dispersion equation. Get solution

12. In writing Eq. (25-3) we neglected to include a contribution due to the magnetic force on the electron. Under what condition is the magnitude of the magnetic force exerted by a harmonic electromagnetic wave on an electron much less than the magnitude of the electric force exerted by the same harmonic electromagnetic wave acting on the electron? (Hint: see Eq. (4-30)). Get solution


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