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 1. The fiber has an index of refraction n. The transmited portion of the beam travels through the fiber and strikes the wall of the fiber at an angle of incidence,  1.

Part A: Find an expression for  sin1 if 1 is equal to the critical angle for total reflection at the fiber wall.

  sin1 = ______________

Part B: 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?

n = _______________

Explanation / Answer

1 is citical angle so,

by snell's law

sin(1) / sin(90) = 1 / n

sin(1) = 1 / n

cos(1) = sqrt(1 - sin(1)^2)

cos(1) = sqrt(1 - (1 / n)^2)

also,

sin(1) / sin(2) = n / 1

2 = pi/2 - 1

sin(1) / sin(pi/2 - 1) = n / 1

sin(90 - x) = cos(x) so,

sin(1) / cos(1) = n

sin(1) = n * cos(1)

sin(1) = n * sqrt(1 - (1 / n)^2)

sin(1) = sqrt(n^2 - 1)

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