Please Help! Snell\'s Law is used here but I need to know what the refractive in
ID: 2019310 • Letter: P
Question
Please Help!Snell's Law is used here but I need to know what the refractive index is for the prism and if the wavelength of red light play's into this as well. PLease help solve this? My guess is that the laser beam does not come outside the other side of the prism due to the angle made by the light inside the prism. Problem below:
A glass prism whose cross section is an equilateral triangle length 9.5 cm is placed flat on a table. A laser whose output is red light at a wavelength 694nm, fires a beam of light at the prism at a distance of 3 cm above the surface of the table. What happens to this light as it passes through and emerges from the prism?
Explanation / Answer
If you need an exact solution you need the particular index of refraction for this glass. Your textbook probably has a general index that it uses for all glass, maybe 1.5, and that maybe is what you are supposed to use for this problem. The wavelength is irrelevant unless you need to be really, really, exact.
Assuming 1.5 is the correct index, and calling the index for air 1, we have
sin 30 degrees = 1.5 sin inside
sin inside = 1/3 so inside = 19.47 degrees
Now this is kind of a non-standard way of looking at it, but consider that the angle with respect to the horizontal that this internal angle makes is -10.53 degrees. The normal is 30 degrees down and the refractive angle is the 19.47. I'm just trying to figure if it makes it all the way across the prism or hits the bottom first.
It makes it across. Let x be the distance where the internal beam finally has dropped 3 cm (which wouuld make it hit the bottom). Then 3/x = tan 10.53 degrees and x 16 cm, more than enough room.
So the beam hits the other side and refracts down even more, first angle is 40.53 degrees so outgoing angle back into air, again using 1.5 as index:
1.5 sin 40.53 = sin out and sin out is about 77 degrees, pretty close to total internal reflection so the answer is pretty sensitive to refractive index.