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 \(l\). The plate is made of non-magnetic substance whose permittivity decreases exponentially from a value \(\varepsilon_{1}\) at the front surface down to a value \(\varepsilon_{2}\) at the rear one. How long does it take a given wave phase to travel across this plate?

Reveal Answer
t=2(ε1ε2)l/cln(ε1/e2)t=2\left(\sqrt{\varepsilon_{1}}-\sqrt{\varepsilon_{2}}\right) l / c \ln \left(\varepsilon_{1} / e_{2}\right)