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set4 - ECE 222B Winter 2010 Homework Set 4 Problems 1 and 2...

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ECE 222B, Winter 2010 Homework Set 4: Problems 1 and 2 are due Tuesday, Feb 17th. 1. We wish to determine what fraction of light in glass (for simplicity, let the permittivity of the glass be ε g = 2 ε 0 ), incident from the left upon an air gap with width is transmitted across the gap into an identical piece of glass. Assume the incident and reflected waves have frequency ω and magnetic fields that are ˆ y -polarized (TM polarization), and that the incidence angle θ i is the critical angle (angle at which total internal reflection first occurs for a single boundary). You may assume that μ = μ 0 in both the glass and gap. (a) What is the load impedance in the gap region? For this part, first write down Z l for arbitrary θ i , then take the limit as θ i approaches the critical angle. (b) Assuming θ i equals the critical angle, what is electric and magnetic field in the gap region? What is the real part of the time-averaged Poynting vector in the gap?
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