Problem 23.40 A beam of light enters the end of an optic fiber as shown in (Figu

Question

Problem 23.40 A beam of light enters the end of an optic fiber as shown in (Figure 1). Part A Show that we can guarantee total internal reflection at the side surface of the material (at point A), if the index of refraction is greater than about 1.42. In other words, regardless of the angle , the light beam reflects back into the material at point A, assuming air outside. What if the fiber were immersed in water? Essay answers are limited to about 500 words (3800 characters maximum, including spaces). 3800 Character(s) remaining

Explanation / Answer

For the critical case,

gamma = critical angle = Arcsin(1/nfiber)

Thus, we can show that

beta = 90 deg - gamma

beta = 90 deg - Arcsin(1/nfiber)

By Snell's law once more,

nair sin(alpha) = nfiber sin(beta)

As nair = 1,

sin(alpha) = nfiber sin(90 deg - Arcsin(1/nfiber))

As sin(90 - C) = cos C,

sin(alpha) = nfiber cos(Arcsin(1/nfiber))

The edge case for alpha is that alpha = 90 deg. Thus, sin alpha = 1,

1 = nfiber cos(Arcsin(1/n))

As cos(Arcsin X) = sqrt(1 - x^2)

Then

1 = nfiber sqrt(1 - 1/nfiber^2)

1 = sqrt(nfiber^2 - 1)

1 = nfiber^2 - 1

nfiber^2 = 2

nfiber = 1.41   [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.