Finding the Velocity of Light through an Unknown substance

[OnceKnown]

Homework Statement

In the above figure, a ray of light is incident upon the interface between two media having indices of refraction n1 = 1.2 and n2, which is unknown. The known angles are f2 = 60° and f3 = 29.9°. (Note that the angles in the diagram may not be accurate.) What is the speed of light in the second medium?

Homework Equations

Snell's Law n_{1}sin θ_{1} = n_{2}sin θ_{2}

And the velocity of light equation:

n = \frac{c}{v_{n}}

The Attempt at a Solution

Since the Angles given aren't the "true" angles that are used in Snell's Law

I took each angle and subtract them from 90° to get θ_{2} = 30° and θ_{3} = 60.1°

From there, I calculated that θ_{1} = 29.9°

I took the variables n_{1} = 1.2 and θ_{1} & θ_{2} and plugged them into the Snell's Formula to get n_{2} = 1.196 as the index of refraction of the unknown substance.

I then plugged that calculation into the velocity formula to get 2.5 x 10^{8}, but I get that as the wrong answer.

I don't know where I went wrong with this. Thank you for your help!

 

[TSny]

I took each angle and subtract them from 90° to get θ_{2} = 30° and θ_{3} = 60.1°

From there, I calculated that θ_{1} = 29.9°

What does the "law of reflection" tell you about θ₁ and θ₃.

 

[OnceKnown]

The Law's of reflection would state that θ_{1} = θ_{3}. I then got the angle as 60.1 degrees. I was looking at the picture incorrectly and used the wrong angles that were required for snell's Law. I got it now!

Thanks TSny!