Light in air ( ) meets BK7 glass ( ) at normal incidence

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Wave propagation and light in media

What an Instrument Can See, Ch The boundary as a two-port

Problem

Light in air (

n_i=1

) meets BK7 glass (

n_t=1.5168

) at normal incidence. Write

E_{1\pm}

for the forward/backward field amplitudes on the air side and

E_{2\pm}

for those on the glass side, and define the interface matrix

D

\begin{pmatrix}E_{2+}\\E_{2-}\end{pmatrix} = D\begin{pmatrix}E_{1+}\\E_{1-}\end{pmatrix},\qquad D = \frac{1}{t'}\begin{pmatrix}1 & -r\\ -r & 1\end{pmatrix},

where

r

t'

are the (real, normal-incidence) Fresnel amplitude coefficients for light incident from air (

r

) and returning from glass (

t'

, the primed transmission coefficient). ((a)) Compute

r

t

and

t'

from the Fresnel formulas at normal incidence. ((b)) Compute

\det D

. ((c)) The paraxial ray-transfer matrix for refraction at any surface (Chapter 1) has determinant exactly

+1

. State whether

\det D=1

here, and explain in one or two sentences why the interface matrix need not share this property even though it is built from the same boundary.