Concept explainers
An optical fiber has an index of refraction n and diameter d. It is surrounded by vacuum. Light is sent into the fiber along its axis as shown in Figure P34.31. (a) Find the smallest outside radius Rmin permitted for a bend in the fiber if no light is to escape. (b) What If? What result does part (a) predict as d approaches zero? Is this behavior reasonable? Explain. (c) As n increases? (d) As n approaches 1? (c) Evaluate Rmin assuming the fiber diameter is 100 μm and its index of refraction is 1.40.
Figure P34.31
(a)
Answer to Problem 35.49P
Explanation of Solution
Given info: The index of refraction is
The figure that represents the given conditions is shown below,
Figure (1)
From figure a ray originally moves along the inner edge will have the smallest angle of incidence when it strikes the outer edge of the fiber in the curve. Thus, if this ray is totally internally reflected, all of the others are also totally reflected.
The necessary condition for the ray to be total internal reflection is,
Here,
For very small value of
The above condition can be written as,
The expression of
Substitute 1 for the value of
The expression of
Here,
The expression of equation (1) becomes.
The minimum value of outside radius permitted for a bend in the fiber is
Conclusion:
Therefore, the smallest outside radius
(b)
Answer to Problem 35.49P
Explanation of Solution
The result from part (a) is,
Here,
The value of
The lesser value of
The thinner the optical fiber, the radius up to which the fiber is bent becomes smaller.
Conclusion:
Therefore, the
(c)
Answer to Problem 35.49P
Explanation of Solution
As
Here,
The above expression can be written as,
It is clear that as
Yes, as
Conclusion:
Therefore, the
(d)
Answer to Problem 35.49P
Explanation of Solution
As
Here,
The above expression can be written as,
It is clear that as
Yes, as
Conclusion:
Therefore, the value
(e)
Answer to Problem 35.49P
Explanation of Solution
Given info: The diameter of the fiber is
Explanation:
The formula to calculate the
Here,
Substitute
Conclusion:
Therefore, the value of
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Chapter 35 Solutions
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