The refractive index of a transparent material can be determined by measuring th
ID: 1446059 • Letter: T
Question
The refractive index of a transparent material can be determined by measuring the critical angle when the solid is in air. If c= 41.2° what is the index of refraction of the material?
A light ray strikes this material (from air) at an angle of 35.2° with respect to the normal of the surface. Calculate the angle of the reflected ray (in degrees).
Calculate the angle of the refracted ray (in degrees).
Assume now that the light ray exits the material. It strikes the material-air boundary at an angle of 35.2° with respect to the normal. What is the angle of the refracted ray?
Explanation / Answer
snell's law
n1*sin A1 = n2*sin A2
A.
When light is incident at the critical angle on the interface between the material and air, the angle of refraction is given by 90 deg
sin 90 = 1
critical angle = 41.2 deg
for air n = 1
using snell's law
n1*sin A1 = n2*sin A2
n1 = 1*sin 90 deg/(sin 41.2 deg)
n1 = 1/sin 41.2 deg
n1 = 1.518
B.
Angle of incidence = angle of reflection
Angle of refliection = 35.2 deg
C. Angle of refraction is given by snell's law
in this case n1 = 1 (air)
A1 = 35.2 deg
n2 = 1.518
A2 = ?
from snell's law
A2 = arcsin ((1*sin 35.2 deg)/1.518)
A2 = 22.31 deg
D. this time
n1 = 1.518
A1 = 35.2 deg
n2 = 1
A2 = ?
A2 = arcsin ((1.518*sin 35.2 deg)/1)
A2 = 61.04 deg
let me know if you have any doubt.
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