An optical fiber has an index of refraction n and a diameter d. it is surrounded

Question

An optical fiber has an index of refraction n and a diameter d. it is surrounded by vacuum. Light is sent into the fiber along its axis as shown in the front figure.

a)Find the smallest outside radius Rmin permitted for a bent in the fiber if no light is to escape

b) What result does part (a) predict as d approaches zero?

c) What result does part (a) predict as n increases?

d) What result does part (a) predict as n approaches 1?

e) Evaluate Rmin assuming the fiber diameter is 100 ?m and its index of refraction is 1.4

Explanation / Answer

the incident angle is given by

a)

(R-d)/R = sin(i)

for the total internal reflection to occur

sin(i) = 1/n

therefore

R = n*d / (n-1)

b)

as d approches 0 then R approches zero

c)

as n increases then R also increases

d)

as n approches 1 then R becomes infinity

e)

R = 1.4 * 100 * 10^-6 / (1.4 - 1)

R = 0.35 mm

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