What Is the Index of Refraction for Each Wavelength in a Prism?

[ghostops]

Homework Statement

A light ray in air strikes the right-angle prism shown in the figure (Figure 1) (∠B=28.0∘). This ray consists of two different wavelengths. When it emerges at face AB, it has been split into two different rays that diverge from each other by 8.50∘ .

Find the index of refraction of the prism for each of the two wavelengths.
Enter your answers in ascending order separated by a comma.

Homework Equations

n^asinΘ_a=n_bsinΘ_b

The Attempt at a Solution

From the Normal I determined that the angles for n₁ and n₂ are 74 and 82.5. However I am running into the issue of where to go from here Also the angle for the incident angle is 62.

I did not know what the index is for the Right angle prism I used 1.5 for glass for it orginally and out with the values 1.38 (74)and 1.34 (82.5). however those were not the correct values.

I do not know where to go from here

thank you in advance

 

[TSny]

Hello, ghostops.

1. The problem statement
Find the index of refraction of the prism for each of the two wavelengths.

Homework Equations

n^asinΘ_a=n_bsinΘ_b

The Attempt at a Solution

From the Normal I determined that the angles for n₁ and n₂ are 74 and 82.5. ... Also the angle for the incident angle is 62.

Your numbers look good to me.

I did not know what the index is for the Right angle prism... I used 1.5 for glass for it

I believe this is what the question is asking you to calculate. Try setting up Snell's law for the ray corresponding to the 12^o angle in the picture. Then repeat for the other ray.