Light is passing through a transparent material at an angle of 63 degrees.  The material has an index of refraction of 1.6.  At what angle will the light pass into the air?

Expert Answers
justaguide eNotes educator| Certified Educator

When a beam of light passes from one medium to another the beam bends if the two mediums do not have the same refractive index.

If the angle of incidence is A and the angle of refraction is B, the two are related as `(sin A)/(sin B) = (n2)/(n1)` where n1 is the refractive index of the first medium and n2 is the refractive index of the second.

In the problem, the angle of incidence A is 63 degrees and the refractive index of the material is 1.6. The refractive index of air is 1. If B is the angle of refraction, `sin 63/sin B = 1/1.6`

=> `sin B = 1.6*sin 63`

=> `sin B = 1.425`

Is is seen that sin B > 1. This indicates that the beam of light does not pass into the air. The beam of light undergoes total internal reflection.

quirozd eNotes educator| Certified Educator

Snell's Law:


let `n_1 = 1.0` (air) and n_2 = 1.6

So, `\theta_1 = 63^o`

Solve for `\theta_2`

`\theta_2 = sin^(-1)(n_1/n_2*sin(\theta_1))`

`\theta_2 =sin^(-1)(1.0/1.6*sin(63^o))`

:. `\theta_2 = 33.8^o`