Optic Calculations

From the data on the TFZ 5b sight below we see that it has light transmission of 20.1%.    That is very low.  It is a wonder why anyone would think that this German sight can be called a clear specimen.  How would these get a reputation of being able to see in low light better than other sights?   link

To see how it may be almost impossible to have such a low transmission figure if there is a coating.  We can try to calculate the light transmission given that we know the light transmission loss from glass and air-glass surfaces.  First of all light loss calculations are multiplication reduction of the original light beam.  So light passing through a glass pane or lens has an affect by multiplying less than 1 .  If the light loss of the first surface is 5% then light loss of the second surface is 5% of the remaining light.  95% x 95% of the light should pass through 0.95^2 or 90.25%.  It is not additive.   

In measuring a French APX L700 direct sight of 14 pairs of air-glass surfaces appears like the total glass a ray passes about 7.9 cm of glass.  Now, modern optical glass loses 2% of the light per cm.  Let's say that WWII glass loses 3% per cm.  For a test lets say a light ray will pass through a total of 9 cm of glass in an articulated German sight.   So there would be on average of 0.6 cm of glass per pair (9/15) of air-glass surfaces.  Or a loss of 1.8% per surface pair.   By our sight page (page 37) we know the ordinary glass loses 4.25% per air-glass surface.  So light loss per lens would be: (100-4.25) /100 x (100-1.8) /100 x (100-4.25) /100.  Or,  90.03% of the light would remain (be transmitted by this one glass object).   If this was the average of 15 glass lenses/prisms it would reduce the light transmission to 20.693%.   

French APX L700 direct sight 14 lenses ,  ~7.9 cm LOS glass.

(0.9003 ^ 15)   Almost the 20.1% of the British evaluated light transmission.  This would mean that this German lens had no coating.    Is that possible?

Take for example the Russian TSh-16 articulated sight of the T-34-85 tank.
It is said to be a copy of the German TZF-5x series sight.  In fact it does have exactly 30 air-glass surfaces (11 lenses/covers and 4 prisms).
This should have about the same light transmission as the German TZF-5b sight.  Indeed captured T-34-85 sights were evaluated by the Finns and was said to be as clear as the sights on the German 75mm model 40 gun, (It would either be the Sfl. ZF 1a StuK gun sight or the TZF-5f tank sight).   Also, said by the Finns to be a great improvement over the sights of the earlier model T-34-76.

Russian Tsh-16 articulated sight for T-34/85 tank.

"Observation devices: the refractive telescopic sight is greatly superior to the sight of the model 1942-1943 T-34 tank. The clarity of the sight is on the level of the German 75 mm model 1940 gun"
Ref link

The Finns also had an opinion on what the thought which gun had the best optics.  Ref link
"While the Germans separated the version used in tanks (7.5 cm KwK 40 L/48) and the version used in assault guns (7.5 cm StuK 40 L/48) as separate gun models, Finnish Army named both versions as 75 Psv.K/40 (75-mm tank gun model 1940). Main gun optics used in these armoured vehicles:
PzKw IVJ gun sight: T.Z.F.5f, magnification 2.4X.
Stu 40 G gun sight: Sfl. ZF. 1a, magnification 5X.

Finnish tank crews noted that from all armoured fighting vehicles in Finnish use during World War 2, Stu 40 G was the one that had the best optics."

The T-34-76 model 1941/42 TMFD sight we have seen were evaluated by the British as having a 39.2% light transmission figure.    The TMFD-7 of similar
characteristics was mounted in the T-34-76 models 1942-1943.

If the Russian Tsh-16 sight is "greatly superior" to the T-34/76 sight how can it only be equivalent to a 20.1% light transmission sight?     20.1% is less than 39.2%.    By the transitive property of mathematics the TZF-5b should have a light transmission value greater than 39.2%.   Something is wrong in the evaluation.   

Maybe the TZF-5b sight the British were evaluating were damaged or they did not adjust it correctly.

Now US technical manual TM 9-258 Elementry Optics December 1977 does indicate the relative worth of coated lenses.