Solving for Initial Angle of Incidence in Total Internal Reflection

[ephdub]

Here's the question:

http://www.geocities.com/rhack_/physics.jpg

I'm doing a CAPA (Computer Assisted Personalized Approach) - basically online assignments. So.. here's one of my questions.. I know that...
in order to have total internal reflection, the angle of incidence for the first internal reflection point must be greater than or equal to the critical angle for the glass. (As the initial angle of incidence increases, so does the angle of refraction, thus the angle of incidence for the internal reflection decreases.)

And that by using the given angles for the prism.. i should be able to calculate the angle of refraction.. and then calculate the intial angle.. I'm sucking it up and I can't get this one.. i should be able to do it with just snell's law..

(n1)[sin(theta1)]=(n2)[sin(theta2)]

any help is much appreciated..

 

[ephdub]

i got up to..

(n1)[sin(theta1)]=(n2)[sin(theta2)]
where n1 = air
n2 = my index

(1)[sin(theta1)]=2.1[sin45]
but the only problem is.. i know that this is wrong.. since (2.1)(sin45) is > 1.. and theta will be messed up on it..

I know it has to do with something with the geometry inside.. but my brain's farting..

 

[wais]

It seems like you have a good understanding of the concept of total internal reflection and Snell's law. In order to find the initial angle of incidence, you can use the formula n1sin(theta1) = n2sin(theta2) and solve for theta1 by plugging in the given values for n1, n2, and theta2. This will give you the angle of refraction, which is equal to the angle of incidence for the first internal reflection point. Then, you can use the relationship between the angle of incidence and the angle of refraction to find the initial angle of incidence. Remember that as the angle of incidence increases, the angle of refraction also increases, so the initial angle of incidence must be greater than or equal to the critical angle for total internal reflection to occur. Keep practicing and you will get the hang of it!