A ray of light is incident at an angle of 51.1� degrees
on the surface of a piece of crown glass whose
index of refraction is 1.52 degrees.
What is the angle of refraction?
Answer in units of �.
Ni*sinAi = Nr*sinAr
That is Snell's law in an easy-to-remember form.
The refractive index N is NOT measured in degrees. It is a dimensionless ratio.
Ni is the index on the air side of the prism, 1.000
Nr is the refractive index of the glass, 1.52
Ai = 51.1 degrees
Solve for Ar, the angle of refrfaction.
sin Ar = (sin 51.1)/1.52
0.51
To determine the angle of refraction, we can use Snell's Law. Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media involved.
Mathematically, Snell's Law is written as:
n1 * sin(θ1) = n2 * sin(θ2)
Where:
n1 and n2 are the indices of refraction of the two media
θ1 is the angle of incidence
θ2 is the angle of refraction
In this case, the angle of incidence (θ1) is given as 51.1 degrees, and the index of refraction (n2) of crown glass is given as 1.52.
Thus, we have:
sin(51.1°) = 1.52 * sin(θ2)
To find the angle of refraction (θ2), we rearrange the equation to isolate sin(θ2):
sin(θ2) = sin(51.1°) / 1.52
Now, we can use an inverse sine function to find the angle of refraction:
θ2 = sin^(-1) (sin(51.1°) / 1.52)
Calculating this expression:
θ2 ≈ sin^(-1) (0.814) ≈ 55.2°
Thus, the angle of refraction is approximately 55.2 degrees.