Index of Refraction in a prism

In summary, the light incident on a 45 degree prism undergoes total internal reflection at point P, and using the formula n2/n1 = sin theta1 / sin theta2, where n1 is air and n2 is the index of refraction for the prism, we can determine that n2 must be equal to 1.41 in order for the total internal reflection to occur. The angles of incidence and refraction are 45 degrees and 90 degrees, respectively.
  • #1
purduegirl
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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.
 
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  • #2
The index of refraction n2/n1 =[tex] \frac{sin \theta_1}{sin \theta_2}[/tex] 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?
 
  • #3
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.
 
  • #4
one will be 45 degrees and the other would be 30 degrees?
 
  • #5
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?
 
  • #6
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?
 
  • #7
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
 
  • #8
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.
 

1. What is the index of refraction in a prism?

The index of refraction in a prism is a measure of how much the speed of light is reduced when passing through the prism. It is a dimensionless quantity and is typically denoted by the symbol "n".

2. How is the index of refraction in a prism calculated?

The index of refraction in a prism can be calculated by dividing the speed of light in a vacuum by the speed of light in the prism material. This can be represented by the equation n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the prism material.

3. What factors can affect the index of refraction in a prism?

The index of refraction in a prism can be affected by several factors, including the type of material the prism is made of, the wavelength of light passing through the prism, and the angle at which the light enters the prism.

4. How does the index of refraction in a prism affect the path of light?

The index of refraction in a prism causes light to bend or refract as it passes through the prism. This is due to the change in speed of light, causing the light to change direction and separate into its component colors.

5. What is the relationship between the angle of incidence and the index of refraction in a prism?

The angle of incidence, or the angle at which light enters the prism, is directly related to the index of refraction. As the angle of incidence increases, the index of refraction also increases, causing the light to bend more and creating a larger separation of colors.

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