Re: Help: rear view mirror optics (fwd)

[Stephen Murray <murray8@LLNL.GOV>]

In my edition of Serway & Beichner, they only discuss the
upwardly-directed dim reflection as being partial reflection from the
front surface, and the brighter reflection from the aluminized mirror
in the back.

I'm suspicious that the lower dim image is the result of three
reflections.  The light which passes through the front surface and
reflects from the aluminized back surface will partially reflect
internally when it again encounters the front surface.  The
internally reflected light will again reflect off of the mirrored
back surface, and most of it (less an internally reflected fraction)
will then exit the front surface, giving the lower dim image.

I may well have blown an angle somewhere, but I drew rays for a wedge
of glass, with the front surface tilted at an angle x relative to the
back, mirrored surface, and started with an incident beam normal to
the front surface.  The bright reflection came out at an angle of 2nx
below that incident beam (n=index of refraction in the glass), and
the second, dim beam came out at 4nx below it.

If I remember my Hecht & Zajac correctly, reflectance depends upon
the difference in the indices of refraction, but not whether you're
going from high to low or vice-versa.  As a result, the fraction of
internally-reflected light will be similar to the fraction of light
initially reflected at the front surface (which gave the upper dim
image).  Assuming that the transmission at the air-glass interface
and the reflectance of the mirrored surface are both fairly high,
then the lower dim image should be almost as bright as the upper one,
as it certainly looks to my uncalibrated and untrained eye.

This predicts that there should be additional images below the lower
dim image, each reduced in brightness by about a factor of the
reflectance at the air-glass interface.  I haven't tried looking for
the first one yet--I wonder if shining a laser pointer into my rear
view mirror will show anything?

> There is a real nice explanation with diagram in Serway and Beichner's
> Physics for Scientists and Engineers (Saunders publishing).  It is
> Conceptual Example 36.3 on page 1143.  It is probably in other Serway
> books as well.
> ...
>
> >>> Robert.Cohen@PO-BOX.ESU.EDU 04/23/02 05:02PM >>>
> I've been unable to find a source that explains both the UPWARDS and
> DOWNWARDS dimming.  Can anybody else?


================================
Stephen D. Murray
Physicist, A Division
Lawrence Livermore National Laboratory
Email:  sdmurray@llnl.gov
Phone: (925) 423-9382
FAX:    (925) 423-0925
================================