"The way single-coatings work is that there are substances that pass
certain wavelengths and reflect others."
This is not _at all_ correct, I'm afraid.
There is no room to go into a detailed explanation of how
anti-reflection coatings work. Here's a simple explantion for
single-layer coatings.
Different substances have different refractive indexes. Glasses have
higher refractive indexes than air (if they didn't, you couldn't make
lenses from them!), so * reflection occurs at the point where the light
enters and leaves the glass. It amounts to about 40f the incident
energy. (That's why you see a faint reflection from a sheet of plain
glass. If you place the glass in water, which has a similar refractive
index, the glass seems to disappear.)
To borrow an exact analogy from electrical engineering, the difference
in refractive index can be viewed as an impedance mismatch that can be
corrected with a quarter-wave stub. In other words, if we coat the lens
with a substance having the right refractive index and a thickness of
one-quarter wave, the reflection will be completely cancelled out and
"all" the incident light will enter (or leave) the lens.
The appropriate refractive index is found by taking the square root of
the product of the refractive indexes of air and the glass in question.
Magnesium fluoride is transparent, has the right index, and will stick
to glass, so it's commonly used for single-layer coatings.
The quarter-wavelength is usually calculated for green light, which
means that red and violet light will still be partially reflected. But
it's still a _big_ improvement over non-coated lenses.
In fact, modern lenses owe their very existance to coating (which came
into wide use after WWII). Prior to coating, lenses often had most or
all of their elements cemented together, to reduce light loss (because
the glasses were more like each other in refractive index than they were
like air). This hurt the lens designer, because lens spacing could not
be used as a parameter in the design, and cemented elements had to have
the same curvatures.
Coating and multi-coating make possible those horribly complex zoom
lenses that keep our gadget bags light. Without coating, the lenses
would be of much lower optical quality, have significantly more flare,
and pass a lot less light -- IF they existed at all.
Multi-coating was developed to give better anti-reflection
characteristics over a wider range of wavelengths. I leave it to an
expert on multi-coating to explain how it works. (Good luck!)
* That "so" covers an awful lot of physics and math. Any physics
textbook discusses this. Try Halliday and Resnick.
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