What is the index of refraction of a material if the angle of indence in air is 50 and the angle of refraction in the material is 40?
n = sin50/sin40
Review Snell's law
To find the index of refraction of a material, you can use Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the reciprocal of the index of refraction of the material.
Mathematically, Snell's law is expressed as:
n1 * sin(θ1) = n2 * sin(θ2)
where:
n1 = index of refraction of the first medium (in this case, air)
θ1 = angle of incidence
n2 = index of refraction of the second medium (the material)
θ2 = angle of refraction
Now, let's plug in the given values:
n1 = 1 (since the index of refraction of air is considered to be 1, approximately)
θ1 = 50 degrees
θ2 = 40 degrees
Using Snell's law, the equation becomes:
1 * sin(50) = n2 * sin(40)
To find n2, we rearrange the equation:
n2 = (1 * sin(50)) / sin(40)
Using a scientific calculator or any calculator that supports trigonometric functions, we can evaluate this expression.
n2 ≈ 1.305
Therefore, the index of refraction of the material is approximately 1.305.
To find the index of refraction of a material, you can use Snell's Law. Snell's Law relates the angle of incidence and the angle of refraction to the index of refraction of the materials involved.
Snell's Law is expressed as:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the index of refraction of the first material (in this case, air)
- n2 is the index of refraction of the second material (the material in question)
- theta1 is the angle of incidence
- theta2 is the angle of refraction
In this problem, we are given:
- theta1 (angle of incidence in air) = 50 degrees
- theta2 (angle of refraction in the material) = 40 degrees
Since the first material is air, the index of refraction for air is almost 1 (approximately 1.00). Therefore, we can substitute the values into Snell's Law:
1.00 * sin(50) = n2 * sin(40)
To find n2 (the index of refraction of the material), re-arrange the equation:
n2 = (1.00 * sin(50)) / sin(40)
Now, use a scientific calculator to calculate this expression:
n2 ≈ 1.244
Therefore, the index of refraction of the material is approximately 1.244.