A plane electromagnetic wave falls normally on a non-magnetic plane-parallel plate of thickness ℓ. Its permittivity decreases exponentially from ε₁ at the front surface to ε₂ at the rear surface. Which expression gives the travel time of a wave phase across the plate?
Options

Question

A plane electromagnetic wave falls normally on a non-magnetic plane-parallel plate of thickness ℓ. Its permittivity decreases exponentially from ε₁ at the front surface to ε₂ at the rear surface. Which expression gives the travel time of a wave phase across the plate?

Options

G1 Physics · Accepted Answer

For a non-magnetic medium, local phase speed is v(x)=c/√εᵣ(x), so dt=√εᵣ(x)dx/c. Integrating the stated exponential profile from 0 to ℓ gives t=2ℓ(√ε₁−√ε₂)/[c ln(ε₁/ε₂)]. Hence option A.