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A beam of light is incident from air on the surface of a liquid. If the angle of incidence is $30.0^{\circ}$ and the angle of refraction is $22.0^{\circ},$ find the critical angle for the liquid when surrounded by air.

$48.75^{\circ}$

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where has to find a critical angle for a liquid when the angle of incidence is 30 degrees and the angle of refraction is 22 degrees. Um, when it's coming from air into that liquid, so in someone is one beta one is 30 degrees and data to is 22 degrees and were asked to find the critical angle or they to see, well, the sign of the critical angle. It's just going to be equal to the ratio of the first medium to the second medium. But we need to know, um, the index of refraction of the second medium in some, too, so that we can go back to Snell's Law, which says the sign of fatal one multiplied by the index of refraction of one so in someone is equal to the in separate index refraction, too. Times to sign faded too. Okay, well, we know they don't want data to, and in some once therefore, weaken sulphur instead, to which is going to be equal to him. Someone times the sign of fate of one divided by the sign of faith, too. Playing all those values into this expression, we find that the index of refraction is equal to 1.33. So then going back up to our expression for the critical angle we find that data see is equal to the inverse sine of in someone to instant, too. We just found index of refraction of medium to instead to so taking the inverse sine of that ratio, we find that this is equal to 48 0.75 degrees. We can go ahead and box that in, is our solution to this question.