@misk94555 Maybe you should ask that as a question on some StackExchange site, maybe physics.stackexchange.com

@misk94555 That's a very good and fundamental question! There are simple approximations that can be used to calculate that as long as the lines of the grating aren't too small. But to get a very precise answer one needs to either measure it or do a very challenging electromagnetic simulation

In practice one looks it up in a book or uses information from a catalog before ordering it, but it can be calculated.

I think you can ask the question "How do Astronomers estimate the amount of reflected light that goes into each order of a hypothetical diffraction grating if they don't have a specific grating for which they can check the specifications?"

Of course, someone may answer "We don't" or "We just assume it's 10 to 50% and worry about the details later" but it is also possible that someone will show the math.

Or alternatively you can ask first in Physics SE. In principle that would be the better place, but in practice sometimes optics questions get ignored there.

I wish there was an Optics SE specific site!!

John Rennie at the Physics chat had pointed out this article, which describes the sinc function: hyperphysics.phy-astr.gsu.edu/hbase/phyopt/gratint.html

@uhoh What kinds of catalogs might have this [empirical?] information? I've looked for data about higher orders in the grating datasheets(Thor, Edmund, Newport). But they don't seem to mention anything about higher orders.