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A fiber optic cable uses total internal reflection. If the refractive index of t

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Question: A fiber optic cable uses total internal reflection. If the refractive index of the core is 1.6 and the cladding is 1.5, what is the critical angle?

Options:

  1. 38.7°
  2. 41.8°
  3. 48.6°
  4. 60.0°

Correct Answer: 38.7°

Solution: 

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.5/1.6) ≈ 38.7°.

A fiber optic cable uses total internal reflection. If the refractive index of t

Practice Questions

Q1
A fiber optic cable uses total internal reflection. If the refractive index of the core is 1.6 and the cladding is 1.5, what is the critical angle?
  1. 38.7°
  2. 41.8°
  3. 48.6°
  4. 60.0°

Questions & Step-by-Step Solutions

A fiber optic cable uses total internal reflection. If the refractive index of the core is 1.6 and the cladding is 1.5, what is the critical angle?
  • Step 1: Understand that total internal reflection occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index.
  • Step 2: Identify the refractive indices given: the core has a refractive index (n1) of 1.6 and the cladding has a refractive index (n2) of 1.5.
  • Step 3: Use the formula for the critical angle (θc): θc = sin⁻¹(n2/n1).
  • Step 4: Substitute the values into the formula: θc = sin⁻¹(1.5/1.6).
  • Step 5: Calculate the value of 1.5/1.6, which is approximately 0.9375.
  • Step 6: Find the inverse sine (sin⁻¹) of 0.9375 using a calculator or trigonometric table.
  • Step 7: The result is approximately 38.7°, which is the critical angle.
  • Total Internal Reflection – The phenomenon where light is completely reflected within a medium when it hits the boundary at an angle greater than the critical angle.
  • Refractive Index – A measure of how much light bends when entering a material; the ratio of the speed of light in a vacuum to the speed of light in the material.
  • Critical Angle – The minimum angle of incidence at which total internal reflection occurs, dependent on the refractive indices of the two media.
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