A ray of light has an angle of incidence of 30.4� degrees
on a block of quartz and an angle of refraction
of 20.7� degrees.
What is the index of refraction for this block
of quartz?
sin 30.4 = N sin 20.7
Solve for the index, N
It's called Snell's Law
This assumes the incident ray is in air or vacuum, where the index is 1.000
To find the index of refraction for the block of quartz, we can use Snell's law, which relates the angles of incidence and refraction to the refractive index of the material.
Snell's law is given by:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
Here, n1 and n2 are the refractive indices of the initial medium (in this case, air) and the medium the light is entering (quartz) respectively.
Given that the angle of incidence is 30.4 degrees and the angle of refraction is 20.7 degrees, we can substitute these values into Snell's law:
n1 * sin(30.4 degrees) = n2 * sin(20.7 degrees)
We know that the refractive index of air is very close to 1 since it is considered a vacuum in many cases. Therefore, we can approximate n1 as 1:
1 * sin(30.4 degrees) = n2 * sin(20.7 degrees)
Now, we can solve this equation for n2:
n2 = (sin(30.4 degrees)) / (sin(20.7 degrees))
Using a calculator, we can find that sin(30.4 degrees) ≈ 0.5113 and sin(20.7 degrees) ≈ 0.3536
So, the index of refraction for the block of quartz is:
n2 = 0.5113 / 0.3536
Calculating this, we find:
n2 ≈ 1.445
Therefore, the index of refraction for the block of quartz is approximately 1.445.