(N.A.) of the fiber. For a cable with a core that has an index of refraction of 1.5 and a cladding with an index of refraction of 1.28, what do you expect the critical angle acrit to be (in degrees)? Cladding- Core → core refracted reflected

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Consider a ray incident on the end of a fiber-optic cable as illustrated in the figure below.
In the experiment, you will explore the behavior of the fiber as a function of the angle of
incidence a. When a ray strikes the end of the fiber it is bent toward the normal. By
Snell's law, the angle inside the core is sin core = (no/n₁) sin a. Once inside the core,
the ray travels until it strikes the cladding of the fiber. The angle of incidence at the
cladding i is the complementary angle of core. If i is a small angle, the ray will propagate
into the cladding and be lost from the fiber. If i is large, however, the ray will be internally
reflected and bounce down the fiber. By Snell's law, the critical angle for the ray to be
internally reflected is sin icrit = n₂/n₁. In the experiment, you cannot directly measure
angles inside the fiber but you can measure a. Using the facts that, (i) for
core = cos i, (ii) the trigonometric identity
complementary angles, sin
cos i = √√1 - sin² i,
shown that sin acrit =
and (iii) the index of refraction of air is no = 1, it can be
n-n2. This quantity is known as the numerical aperture
(N.A.) of the fiber. For a cable with a core that has an index of refraction of 1.5 and a
cladding with an index of refraction of 1.28, what do you expect the critical angle acrit to
be (in degrees)?
Cladding →→
Core →→
α
ecore
refracted
reflected
Transcribed Image Text:Consider a ray incident on the end of a fiber-optic cable as illustrated in the figure below. In the experiment, you will explore the behavior of the fiber as a function of the angle of incidence a. When a ray strikes the end of the fiber it is bent toward the normal. By Snell's law, the angle inside the core is sin core = (no/n₁) sin a. Once inside the core, the ray travels until it strikes the cladding of the fiber. The angle of incidence at the cladding i is the complementary angle of core. If i is a small angle, the ray will propagate into the cladding and be lost from the fiber. If i is large, however, the ray will be internally reflected and bounce down the fiber. By Snell's law, the critical angle for the ray to be internally reflected is sin icrit = n₂/n₁. In the experiment, you cannot directly measure angles inside the fiber but you can measure a. Using the facts that, (i) for core = cos i, (ii) the trigonometric identity complementary angles, sin cos i = √√1 - sin² i, shown that sin acrit = and (iii) the index of refraction of air is no = 1, it can be n-n2. This quantity is known as the numerical aperture (N.A.) of the fiber. For a cable with a core that has an index of refraction of 1.5 and a cladding with an index of refraction of 1.28, what do you expect the critical angle acrit to be (in degrees)? Cladding →→ Core →→ α ecore refracted reflected
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