Question
Asked Dec 25, 2019
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Endoscopes are medical instruments used to examine
the gastrointestinal tract and other cavities inside the body.
The light required for examination is conducted from an outside
source along a long, flexible bundle of optical fibers to
the tip, where it exits and illuminates the internal cavity. A lens
on the tip collects an image of the lighted cavity and another
fiber bundle conducts the image back along the endoscope
to an eyepiece for viewing (Fig. P22.52). If each fiber in the
bundle has diameter d = 1.00 x 10-4 m and refractive index
n = 1.40, find the smallest outside radius R permitted for a
bend in the fiber if no light is to escape.

Eyepiece
Light
Tip of
endoscope
R
d.
Figure P22.52
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Eyepiece Light Tip of endoscope R d. Figure P22.52

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Expert Answer

Step 1

Given,

Diameter of each fibre in the bundle, d = 1.00×10-4m.

Refractive index, n = 1.40

Step 2

Here,

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e2C sin e2C

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Step 3

Thus,

...
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R-d 1 R nR -nd 2 R R(n-1) 2 nd nd Rmin 2 n-1

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Ray Optics

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