A ray of light of vacuum wavelength 550 nm traveling in air enters a slab of transparent material. The incoming ray makes an angle of 34.3◦ with the normal, and the refracted ray makes an angle of 18.9◦ with the normal. Find the index of refraction of the transparent material. (Assume that the index of refraction of air for light of wavelength 550 nm is 1.00.)

To find the index of refraction of the transparent material, we can apply Snell's Law, which relates the angles of incidence and refraction of a ray of light passing through the boundary between two media:

n1 * sinθ1 = n2 * sinθ2

Where:
- n1 is the index of refraction of the first medium (in this case, air)
- n2 is the index of refraction of the second medium (the transparent material)
- θ1 is the angle of incidence (34.3° in this case)
- θ2 is the angle of refraction (18.9° in this case)

Given that the index of refraction of air is 1.00, we can substitute its value into the equation:

1.00 * sin34.3° = n2 * sin18.9°

Now, let's solve this equation to find the index of refraction of the transparent material:

sin34.3° / sin18.9° = n2

Using a calculator:

0.5576 / 0.3239 = n2

n2 ≈ 1.7205

Therefore, the index of refraction of the transparent material is approximately 1.7205.

To solve this problem, we can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two materials involved.

Snell's law states:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
n1 and n2 are the indices of refraction of the first and second materials
θ1 and θ2 are the angles of incidence and refraction, respectively.

In this case, we have:

n1 = 1.00 (index of refraction of air)
θ1 = 34.3° (angle of incidence)
θ2 = 18.9° (angle of refraction)

Let's plug in the values into Snell's law and solve for n2:

1.00 * sin(34.3°) = n2 * sin(18.9°)

n2 = (1.00 * sin(34.3°)) / sin(18.9°)

Using a calculator, we get:

n2 ≈ 1.57

Therefore, the index of refraction of the transparent material is approximately 1.57.

1.00*sin34.3 = N* sin18.9

Solve for N, the index of refraction in the transparent solid material

N = 1.74