Physics Problem Help?

[MAK1186]

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Hey guys! I am taking Physics II now and I am having trouble figuring out this problem. I have the answer but nothing I do seems to get it. I thought maybe one of you MCAT scholars could help me out lol. Thanks in advance!!

Determine the maximum angle for theta for which the light rays must be incident on the end of a solid glass rod so that total internal reflection will occur along the walls of the glass rod. Assume that the glass rod has an index of refraction of 1.36 and the outside medium is air.

The answer is 67.2 degrees.

 

[HawkeyePostOp]

maybe there are more details in this problem and it's 67 degrees relative to something else, but it looks like the problem is just wrong. It should be 47.

 

[Quantum Chem]

Yeah, looks like the answer is wrong. Using Snell's Law n1sin1(theta) = n2sin2(theta), the answer would be the inverse sine of 1/1.36, which is 47.

sin1(theta) = (n2/n1)sin2(90)
sin1(theta) = (1/1.36)*1
theta = sin-1 (1/1.36)

 

[nfg05]

You guys have solved for what angle the ray must approach the wall to be totally internally reflected, but the problem asks for what angle it must be incident on the end of the rod. The situation is kinda tough to explain verbally so I just drew it out (please excuse my crappy 5 year old scanner). Also, the way I drew it the ray happens to look like it's comin in through the outer rim of the end of the rod, but it doesn't have to be that way. You can move the incident ray anywhere around the face of the end of the rod and the result will be the same.

http://www.duke.edu/~mpj7/PhysProb.pdf

The 47.3 degree angle in the diagram was obtained from the method used by hawkeye and quantum.

edit: http://rapidshare.de/files/39953340/PhysProb.pdf.html mirror if above link doesn't work.

 

[MAK1186]

Ok, yea I was getting 47 too but I see now that was just the first half of the problem. Thanks so much for the explanation and diagram!!

 

[nfg05]

no problem at all, glad I could help