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Stella [2.4K]
3 years ago
7

A glass optical fiber is used to transport a light ray across a long distance. The fiber has an index of refraction of 1.550 and

is submerged in ethyl alcohol, which has an index of refraction of 1.361. What is the critical angle (in degrees) for the light ray to remain inside the fiber?
Physics
1 answer:
devlian [24]3 years ago
6 0

To solve this exercise it is necessary to apply the concepts related to the Snells law.

The law defines that,

n_1 sin\theta_1 = n_2 sin\theta_2

n_1 = Incident index

n_2 = Refracted index

\theta_1 = Incident angle

\theta_2 = Refracted angle

Our values are given by

n_1 = 1.550

n_2 = 1.361

\theta_2 =90\° \rightarrowRefractory angle generated when light passes through the fiber.

Replacing we have,

(1.55)sin \theta_1 = (1.361) sin90

sin \theta_1 = \frac{(1.361) sin90}{(1.55)}

\theta_1 =sin^{-1} \frac{(1.361) sin90}{(1.55)}

\theta_1 =61.4\°

Now for the calculation of the maximum angle we will subtract the minimum value previously found at the angle of 90 degrees which is the maximum. Then,

\theta_{max} = 90-\theta \\\theta_{max} =90-61.4\\\theta_{max}=28.6\°

Therefore the critical angle for the light ray to remain insider the fiber is 28.6°

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