An optical fiber is made of clear plastic with index of refraction n = 1.52.For what angles with the surface will light remain within the plastic "guide"?
A) ϕ

Question

An optical fiber is made of clear plastic with index of refraction n = 1.52.For what angles with the surface will light remain within the plastic "guide"?
A) ϕ < 33.3°
B) ϕ < 59.2°
C) ϕ < 41.1°
D) ϕ < 48.9°
E) ​ϕ < 70.0°

Quizplus · Accepted Answer

Light will remain within the plastic guide as long as it undergoes total internal reflection. The critical angle for total internal reflection is given by sin⁡θ_c=n_2/n_1, where n_1 is the index of refraction of the medium where the light is coming from and n_2 is the index of refraction of the medium where the light is going to. In this case, since the light is coming from air (which has an index of refraction very close to 1) and going into the plastic fiber (which has an index of refraction of 1.52), we have sin⁡θ_c=n_air/n_plastic=1/n_plastic. Therefore, θ_c=sin⁻¹⁡(1/n_plastic)=sin⁻¹⁡(1/1.52)≈48.9°. Any angle of incidence greater than this critical angle will result in the light being refracted out of the fiber.

An Optical Fiber Is Made of Clear Plastic with Index