Two glass prisms of refractive index are separated by a thin air gap of thickness

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Modes, Packets and Media, Ch Reflection, transmission, matching and tunnelling at boundaries

Problem

Two glass prisms of refractive index

n=1.60

are separated by a thin air gap of thickness

d

. Light of vacuum wavelength

\lambda=600\,\mathrm{nm}

inside the first prism strikes the gap at an angle of incidence

\theta = 50^\circ

, beyond the critical angle, so total internal reflection would occur for an infinite gap. In the gap the field decays as

e^{-\alpha z}

with

\alpha = k_0\sqrt{n^2\sin^2\theta-1}

k_0=2\pi/\lambda

, and the power transmitted across a gap of thickness

d

falls as

e^{-2\alpha d}

. Find the gap thickness

d

at which the transmitted power is

1\%

of the power that would arrive if the second prism were in contact with the first.