Finding Critical Angle: A Freshwater Pond Problem

[Liger20]

Homework Statement

Hey, I’m a little bit confused on an optics question on how to find the critical angle when given the indices of refraction for two different mediums. The question deals with a laser beneath the surface of a freshwater pond. The indices of refraction are r=1.33 for the water and s=1.00 for the air. The laser strikes the surface at an angle of 30.0 degrees relative to the perpendicular. I’m asked what angle the beam will emerge from the surface into the air.
You use Snell’s law for this, and the solution in the book I have is as follows:

Homework Equations

sin y/sin x=r/s (the equation for Snell’s Law)

sin y/(sin 30.0 degrees)= 1.33/1.00

sin y/0.500=1.33

sin y= 1.33 x 0.500= 0.665

I understand the problem up to here, but then things get weird:

y=sin-1 0.665=41.7 degrees

The Attempt at a Solution

Whenever I type sin-1 0.665 I get .72749. I am not sure how to actually convert this number into degrees. I think that it’s something simple, but I’d really appreciate it if someone told me what I’m supposed to do. I hope I’ve been specific enough, but if not, just let me know. Thanks!

 

[cryptoguy]

Type in whatever you got on your calculator (.72749) and multiply that by (180/pi)

 

[Liger20]

Whoa, it works! Thank you so much! I wonder why the author didn't say anything about that...