I often read in various forums (fora) that ordinary people attribute greater brightness to binoculars with BaK-4 (Ba = Barium) prisms, compared to those with BK-7 (B = Boron).
But in reality, BK-7 glass is more transparent than BaK-4 glass and we can take an example from SCHOTT's list of new HT and Ultra-HT glasses.

These "T**" transmittance data, are valid for 400nm and 10mm thickness, but by averaging the data from the complete tables and adjusting the thickness for ~ 100mm of glass (more typical of a Porro-prism system), the values of transmittance they become ~ 98% for BK7 and ~ 93% for BaK-4.
Obviously, the BaK-4 glass is the most used in prisms, because it facilitates the reduction of weights and dimensions, in the construction of binoculars of the same size.
But it is certainly not the brightest! 
You're not the first person to argue this point here in the forum. The problem is that when you start applying all your physics to vintage porro 1 binoculars, it never seems to work out the way you describe it. You can certainly state your point and show your numbers to "prove" it, but real life has already taught us otherwise, so we choose not to believe you.
And here's why...
Go back into the mid to late 1950's and start working your way forward. Look at a few of the best binoculars made, and then look at some of the worst. And look specifically for those with the brightest images, and then look for those with the dullest images. What we have found is that the vast majority of those binoculars with the brightest images just happened to also have BaK4 prisms. And the vast majority of those with the dullest images just happened to have Bk7 prisms.
What we have seen is that the best binocular manufactures tended to use BaK4 prisms in their best binocular models. We also have seen that cheaper binoculars were almost universally made with Bk7 prisms. So the argument that BaK4 prisms are brighter, and that Bk7 prisms are not brighter, makes a whole lot more sense in the real world.
And I'll go one step further with this. While it's difficult to find the perfect test for this, because only a few vintage binoculars were made exactly the same except with the two different prisms. But there were a few that would allow for direct comparison. One of these is the Kowa wide angle 7x35 binocular, mentioned by Pat above. There is a Bk7 version and a BaK4 version. I've had both out under the stars in direct comparison with one another. The BaK4 version was clearly brighter than the Bk7 version. And I repeated the test multiple times. I also did this test with Fuji and Kowa standard angle Featherlights. The difference was less pronounced, but the BaK4 versions were still clearly brighter.
So that's why I will always recommend a BaK4 vintage binocular for the brightest images. Because it's true!
Edited by SMark, 11 July 2021 - 07:28 PM.