A p-polarised plane wave of unit amplitude is incident from medium 1 (real index )…

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

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

Problem

A p-polarised plane wave of unit amplitude is incident from medium 1 (real index

n_1

) onto medium 2 (real index

n_2

) at angle

\theta_i

, refracting at

\theta_t

with

n_1\sin\theta_i=n_2\sin\theta_t

; write

r_p,t_p

for the reflection and transmission amplitude coefficients of this process, and

r_p',t_p'

for the same interface traversed the other way, i.e. a p-polarised wave incident from medium 2 at

\theta_t

onto medium 1. ((a)) Time-reverse the first process: reverse the direction of travel of the incident, reflected and transmitted waves (for a real, lossless interface the coefficients are unaffected by this). Write the resulting situation as the superposition of two waves separately incident on the interface, and use linearity together with the fact that the reversed situation contains no wave leaving into medium 2, to derive the Stokes relations

r_p'=-r_p

and

t_pt_p'=1-r_p^2

. ((b)) Air (

n_1=1

) meets BK7 glass (

n_2=1.5168

) at

\theta_i=60.0^\circ

, for which the sign convention adopted throughout gives

r_p=+0.0395

and

t_p=0.6332

(with

\theta_t=34.80^\circ

from Snell's law). Use the Stokes relations to predict

r_p'

and

t_p'

for light incident from inside the glass at

34.80^\circ

, and check your value of

t_p'

against the direct formula

t_p' = 2n_2\cos\theta_t/(n_2\cos\theta_i+n_1\cos\theta_t)

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