# Prism index of refraction

1. May 18, 2006

### jimmy_neutron

This figure shows a laser beam coming from the left, deflected by a 30o – 60o – 90o prism. What is the prism’s index of refraction?

So the index of refraction is = c/v but i dont see how that would help in this question. Can someone help me out on which equation to use.

2. May 18, 2006

### Hootenanny

Staff Emeritus
Try snell's law, with a little bit of trig mixed in

~H

3. May 18, 2006

### jimmy_neutron

Trig is not a word I like to hear

Snell's law: n1 sin theta1 = n2 sin theta 2
I assume that 22.6 degrees is either theta 1 or 2, but i dont know the other, and there are 2 index's of refraction in the equation but both are unkown?

4. May 19, 2006

### Hootenanny

Staff Emeritus
I think it is safe to assume in this case that the refractive index of the area outside the prism is 1. This is the refractive index of a vacuum and is aproximatly equal to the refractive index of air (1.0008). You can find the angle of incidence by simple maths (no trig required sorry). Now if you form a triangle with the horizontal ray and the top of the prism you can say that the angle to the bottom right is 60O, because of similar triangles. Now you need to find the angle between the ray and the normal which is perpendicular to the hypotenues of the prism. If you draw on the normal and lable the angles, it becomes obvious what the angle of incidence is...

~H

5. May 19, 2006

### jimmy_neutron

Ah I see now, thank you for your help!

6. May 20, 2006

### willydavidjr

Yah, suppose the index of refraction of n1 is 1. Then compute using snell's law.

7. May 20, 2006

### Hootenanny

Staff Emeritus
Sorry for the slight correction, but one should assume n2 = 1. n1 is the refractive index of the prism, which the question requires you to determine.

~H

8. Jun 16, 2011

Wait, didn't you have it right the first time? We assume n1=1. Therefore n2/n1=n2=sintheta1/sintheta2. that way theta1=($\delta$/2) + ($\Phi$/2). or am I mixing up my geometry. lol, I haven't taken geometry since grade school so i could be mistaken...