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I'm supposed to write a physics essay and I'm have to describe something that occurs when light hits an interface with a very specific angle. So the sentence goes: "(...) at the critical angle" or "(...) on the critical angle"?

There is a general rule for this or each case is a different case?

Thank you very much.

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    Idiomatically, it would be at. The angle isn't a surface which can be rested "on", it's a point along a continuum of choices, "at" which you can be.
    – Dan Bron
    Mar 4, 2016 at 18:55
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    Optics eh? I agree with the commenter above, it should be 'at'. However I have seen both.
    – la femme cosmique
    Mar 4, 2016 at 18:57
  • I'd second at. Like At right angles to ..
    – R.S.
    Mar 4, 2016 at 18:59
  • I've never heard of using 'on' for this, though all my experience is from physics coursework, so maybe I have a narrow view. Can you provide an actual example where someone uses 'on'?
    – childofsoong
    Mar 4, 2016 at 19:13

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Actually, Google gives about 3 million hits for "on an angle" and about 36 million for "at an angle," which would suggest that both are grammatically correct, but that the latter sees far more frequent use. In general use, I'd say both are acceptable. But if you're writing a physics essay, you might want to stick with the more discourse specific "at," as others have suggested.

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