A laser beam is being shot through two different materials that have been stuck together. if theta 1 = 65.5 and theta 2 = 49.8 what is the index of refraction? (I got 1.2 which is correct) but cant get part 2

PART 2~ If the index of refraction of n3 is 3.6, what is the final angle of transmitting light theta 3?

THANKS IN ADVANCE FOR ANY HELP!
Zach

To find the index of refraction (n) of a material, you can use Snell's Law, which states that the ratio of the sines of the angles of incidence (θ1) and refraction (θ2) is equal to the ratio of the velocities of light in the two materials:

n1 * sin(θ1) = n2 * sin(θ2)

In this case, you have θ1 = 65.5 degrees and θ2 = 49.8 degrees. You also have n1 and n2 as unknowns. Let's assume n1 is the index of refraction of the first material and n2 is the index of refraction of the second material.

Based on your given values, the equation becomes:

n1 * sin(65.5) = n2 * sin(49.8)

Since the two materials are stuck together, the index of refraction does not change within the combined material. Therefore, n1 = n2.

Next, to find the final angle of transmitting light (θ3), you need to use Snell's Law again. You are given the index of refraction (n3 = 3.6) and you want to find θ3.

n2 * sin(θ2) = n3 * sin(θ3)

Substituting n2 as n1 (since they are the same index of refraction), the equation becomes:

n1 * sin(θ2) = n3 * sin(θ3)

But since n1 = n2, we can rewrite the equation as:

n2 * sin(θ2) = n3 * sin(θ3)

Now you can substitute the known values:

sin(49.8) = (3.6) * sin(θ3)

Solve for sin(θ3) by dividing both sides of the equation by (3.6):

sin(θ3) = sin(49.8) / (3.6)

Now you can take the inverse sine of both sides to find θ3:

θ3 = arcsin(sin(49.8) / (3.6))

Calculate the right-hand side to find θ3.