All Problems

Electromagnetic Waves. Radiation

Problem 4.190

A plane electromagnetic wave falls at right angles to the surface of a plane-parallel plate of thickness ll. The plate is made of non-magnetic substance whose permittivity decreases exponentially from a value ε1\varepsilon_{1} at the front surface down to a value ε2\varepsilon_{2} at the rear one. How long does it take a given wave phase to travel across this plate?

Reveal Answer
t=2(ε1−ε2)l/cln⁡(ε1/e2)t=2\left(\sqrt{\varepsilon_{1}}-\sqrt{\varepsilon_{2}}\right) l / c \ln \left(\varepsilon_{1} / e_{2}\right)
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