# Homework Help: Index of refraction of the prism

1. Aug 19, 2009

### {smile}

1. The problem statement, all variables and given/known data
5) A beam of monochromatic light enters an equilateral triangular prism at an angle of incidence of 30.0º. If the index of refraction of the prism is 1.53, at what angle with respect to the surface of the prism does the beam emerge from the other side of the prism?

2. Relevant equations

3. The attempt at a solution
i tried drawing it out, but i have absolutely no idea.

2. Aug 19, 2009

### Staff: Mentor

Re: angles

Show us a drawing and your work. A "relevant equation" might be _____'s Law, eh?

3. Aug 19, 2009

### jgens

Re: angles

Use Snell's Law: $n_1\sin{\theta_1} = n_2\sin{\theta_2}$

4. Aug 19, 2009

### {smile}

Re: angles

i dont know how to draw on here. :( and Snells law right? i cannot figure out how to do that. if Sin(feta)1/Sin(feta)2 = N2/N1, i only have two of the variables! dont i at least need three?

5. Aug 19, 2009

### Staff: Mentor

Re: angles

6. Aug 19, 2009

### jgens

Re: angles

Assume that the ray of light is initially in air. The index of refraction in air is approximately one. Also, the symbol $\theta$ is called theta, not feta.

7. Aug 19, 2009

### {smile}

Re: angles

we dont know Sin(feta) 1 or N1. we only know the angle of refraction and the index of refraction.

8. Aug 19, 2009

### {smile}

Re: angles

so sinθ/Sin30=1.53/1
=1.53sin(30)??

9. Aug 20, 2009

### {smile}

Re: angles

ok let me try this again,

2. Relevant equations
N1sinθ=N2sinθ

3. The attempt at a solution
The light will enter the prism and refract, cross the prism, hit the other side, exit and refract. so there will be lots of angles for me to find, i jsut dont know how to solve for them except for this one.

N1sinθ=N2sinθ
Θ2=sin-1((1.0003)(sin30)/1.53)
Θ= 19 degrees

10. Aug 20, 2009

### drizzle

Re: angles

hey {smile}

you need to sketch so you can understand it well, you need to do it twice [Snell's Law] so you can get the angle of the emerged beam with respect to the surface of the prism [it’s theta 3], try to work out the other theta illustrated in the figure.

http://img197.imageshack.us/img197/1777/13527457.jpg [Broken]

Last edited by a moderator: May 4, 2017
11. Aug 20, 2009

### kuruman

Re: angles

Note that, in the above drawing, θ1 and θ3 are defined in such a way that Snell's Law should be written in terms of their cosines on the "air side" of the ray.

12. Aug 20, 2009

### drizzle

Re: angles

you’re right [we’ll get the same answers], but according to Snell's law, these angles are measured with respect to the normal lines which is perpendicular to the boundaries [that’s why I drew them, but then forgot about them:tongue:], anyhow, here’s the exact one;

http://img30.imageshack.us/img30/1359/10703724.jpg [Broken]

Last edited by a moderator: May 4, 2017
13. Aug 20, 2009

### kuruman

Re: angles

Great. Now see if you can find what the sum of the two internal angles is

θ2 + θ = ?

This will help you connect the first angle of refraction θ2 to the internal angle of incidence θ.

14. Aug 20, 2009

### kuruman

Re: angles

Theta, feta what's the difference - it's all Greek anyway. :rofl:

15. Aug 20, 2009

### drizzle

Re: angles

was that directed to me?

I'm only helping the OPer

16. Aug 20, 2009

### kuruman

Re: angles

It was directed to {smile} who I believe is trying to solve this.