Index of Refraction in a prism

[purduegirl]

Homework Statement

The light incident on a 45 degree prism undergoes total internal relfection at point P. What can you conclude about the index of refraction in the prism? (Determine either a minimum or maximum)


This is a right triangle, with the two other angles being 45 degrees and point is half on the hypotenuse.

The Attempt at a Solution

The answer in the back of the book is 1.41. I have no idea how they came up with this. Could someone explain about they found this number.

 

[cryptoguy]

The index of refraction n2/n1 =$$\frac{sin \theta_1}{sin \theta_2}$$ where theta 1 and theta 2 are the angles from the line normal to the surface (prism). Note that n1 (air) = 1 (for some reason it's not letting me edit the latex)

theta 1 will be the angle the light ray in air makes with the normal, and theta 2 will be the angle it makes with the normal in the prism. So what will theta 1 and 2 equal?

 

[LowlyPion]

Start with what you do know.

An interesting thing to wonder might be what kind of change in index of refraction at the boundary of the prism could affect such a change in angle? Are there any formulas covered in the chapter that might help you in this regard?

Edit: I see someone has already provided you with the formula even while I was typing my message. You should be well on your way.

 

[purduegirl]

one will be 45 degrees and the other would be 30 degrees?

 

[cryptoguy]

Why would it be 30? If there is total internal reflection, the light beam travels along the edge of the prism (in the miminum case). So what would the 2nd angle be?

 

[purduegirl]

From my book, I found that as the angle of incident is increased, the angle of refraction evenutally reaches 90. At 90, it just moves along the surface. So with what your saying, the other angle would be 45 degrees, right?

 

[purduegirl]

n1 = air = 1
n2 = glass ( assuming that the prism is glass)
Sin theta 1 = 45 degrees
sin theat 2 is = degrees

formula used n2 = n1*sin theta 1 / sin theta 2

n2 = (1)*sin 45/sin theta 2

 

[cryptoguy]

If you're saying n2 = glass, then theta1 should be the refracted angle. Remember, your angles start at your normal line, that is at 90 degrees to the surface of the prism. If the light moves along the surface, what is theta1? Then theta2 is going to be the incident ray's angle, which, as you said will be 45 degrees.