The beam from a green laser pointer is traveling in air when it strikes the end

Question

The beam from a green laser pointer is traveling in air when it strikes the end of an optical fiber at an angle of incidence theta1. The fiber has an index of refraction n. The transmitted portion of the beam travels through the fiber and strikes the wall of the fiber at an angle of incidence, phi1.Find an expression for sin theta 1 if phi 1 is equal to the critical angle for total reflection at the fiber wall. Express your answer in terms of the index of refraction, n. What is the minimum value of n for which incoming light at any incident angle will be internally reflected at the wall of the fiber and, therefore, be captured by the fiber? Express your answer using 3 significant figures.

Explanation / Answer

According to snell's law

n1*sin(theta1) = n2*sin(theta2)

n1 is the refractive index of air = 1

n2 is the refractive indedx of fiber = n

then using snell's law

1*sin(theta1) = n*sin(phi1)

sin(theta1) = n*sin(phi1)

but this is equal to n*sin(phi1) = n3*sin(90)

n3 is the refractive index of air = 1

then n*sin(phi1) = 1

then n = 1/sin(phi1) for total internal reflection

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