An unknown material is submerged in a fluid with an index of refraction of 1.33. If a ray of light is incident on the block at 45-degrees and the angle of refraction is 30-degrees. What is the index of the unknown material?
To find the index of the unknown material, 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 two materials,
θ₁ is the angle of incidence, and
θ₂ is the angle of refraction.
In this case, we know the following:
- The index of refraction of the fluid is 1.33 (n₁ = 1.33)
- The angle of incidence is 45 degrees (θ₁ = 45°)
- The angle of refraction is 30 degrees (θ₂ = 30°)
Let's substitute the known values into Snell's Law and solve for the unknown index of refraction (n₂):
n₁ sin(θ₁) = n₂ sin(θ₂)
1.33 * sin(45°) = n₂ * sin(30°)
To find the value of sin(45°), we can use the fact that sin(45°) = √2 / 2:
1.33 * (√2 / 2) = n₂ * sin(30°)
Now, let's solve for n₂:
n₂ = (1.33 * (√2 / 2)) / sin(30°)
To find the value of sin(30°), we can use the fact that sin(30°) = 1 / 2:
n₂ = (1.33 * (√2 / 2)) / (1 / 2)
Simplifying further:
n₂ = (1.33 * √2) / (1 / 2)
n₂ = (1.33 * √2) * 2
n₂ = 1.33 * √2 * 2
n₂ = 2.98
Therefore, the index of the unknown material is approximately 2.98.