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If the refractive index of diamond is 2.42, what is the critical angle for total

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Question: If the refractive index of diamond is 2.42, what is the critical angle for total internal reflection when light travels from diamond to air?

Options:

  1. 24.4°
  2. 30.0°
  3. 36.9°
  4. 41.8°

Correct Answer: 24.4°

Solution: 

Using the formula sin(θc) = n2/n1, where n1 = 2.42 (diamond) and n2 = 1.00 (air), we find θc ≈ 24.4°.

If the refractive index of diamond is 2.42, what is the critical angle for total

Practice Questions

Q1
If the refractive index of diamond is 2.42, what is the critical angle for total internal reflection when light travels from diamond to air?
  1. 24.4°
  2. 30.0°
  3. 36.9°
  4. 41.8°

Questions & Step-by-Step Solutions

If the refractive index of diamond is 2.42, what is the critical angle for total internal reflection when light travels from diamond to air?
  • Step 1: Understand the problem. We need to find the critical angle for light moving from diamond to air.
  • Step 2: Know the refractive indices. The refractive index of diamond (n1) is 2.42 and for air (n2) it is 1.00.
  • Step 3: Use the formula for critical angle: sin(θc) = n2/n1.
  • Step 4: Substitute the values into the formula: sin(θc) = 1.00 / 2.42.
  • Step 5: Calculate the value: sin(θc) ≈ 0.4132.
  • Step 6: Find the critical angle θc by taking the inverse sine (arcsin) of 0.4132.
  • Step 7: Calculate θc ≈ 24.4°.
  • Refractive Index – The refractive index is a measure of how much light bends when entering a material. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.
  • Total Internal Reflection – Total internal reflection occurs when light attempts to move from a denser medium to a less dense medium at an angle greater than the critical angle, resulting in all the light being reflected back into the denser medium.
  • Critical Angle – The critical angle is the angle of incidence above which total internal reflection occurs. It can be calculated using the refractive indices of the two media involved.
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