Half-silvered rear surface phase shift

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SUMMARY

The discussion centers on the phase shift of reflections from half-silvered mirrors, specifically contrasting dielectric and metallized mirrors. It is established that dielectric mirrors do not induce a phase shift upon rear surface reflection, while metallized mirrors can induce a phase shift of 180 degrees or transition continuously to this value with increased metallization. The phase shifts of transmitted and reflected waves must be +π/4 and -π/4, respectively, to satisfy boundary conditions, indicating that the mirror functions similarly to a 90° hybrid junction in microwave applications. The confusion arises regarding the differences in phase shifts between front surface mirrors and dielectric rear surface mirrors.

PREREQUISITES
  • Understanding of wave optics principles
  • Familiarity with half-silvered mirrors and their applications
  • Knowledge of phase shifts in reflection and transmission
  • Basic concepts of microwave hybrid junctions
NEXT STEPS
  • Research the phase shift characteristics of metallized mirrors
  • Study the behavior of dielectric mirrors in optical applications
  • Explore the principles of microwave hybrid junctions
  • Investigate the differences in phase shifts for various types of mirrors
USEFUL FOR

Optical engineers, physicists, and anyone involved in the design and application of optical devices, particularly those working with mirrors and phase shift phenomena.

Alfred Cann
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I have read that the rear surface reflection of a half-silvered mirror undergoes no phase shift. But they caution that this is true only for a dielectric mirror. What is the answer for a metallized mirror? It seems to me that the answer must either be 180 degr., or pass continuously to 180 degr. as we increase the metallization to 100%.
 
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I think I can partly answer my own question.
The amplitudes of the transmitted and reflected waves must both be 1/√2. To satisfy the boundary conditions, their phase shifts must be + and - π/4, so that they add up to match the input wave, 1.0 at zero phase.
Thus, the mirror acts like a 90° hybrid junction, a device well-known in the microwave world.

I would be comfortable with this explanation except for one thing. I can't see how the answer would be any different for a front surface mirror and a dielectric rear surface mirror, yet the literature sez it is. What am I doing wrong?
 

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