A glass optical fiber is used to transport a light ray across a long distance. The fiber has an index of refraction of 1.540 and is submerged in glycerin, which has an index of refraction of 1.473. What is the critical angle (in degrees) for the light ray to remain inside the fiber

73.13°

Explanation:

According to snell's law,

n1sinθi = n2sinθr

n1/n2 = sinθr/sinθi

Critical angle is the angle of incidence at the denser medium when the angle of incidence at the less dense medium is 90°

This means i=C and r = 90°

The Snell's law formula will become

n1/n2 = sinC/sin90°

n2/n1 = 1/sinC

Where n1 is the refractive index of the less dense medium = 1.473

n2 is the refractive index of the denser medium = 1.540

Substituting the values in the formula,

1.540/1.473 = 1/sinC

1.045 = 1/sinC

SinC = 1/1.045

SinC = 0.957

C = sin^-1(0.957)

C = 73.13°

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