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If the refractive index of a medium is 2.0, what is the maximum angle of inciden

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Question: If the refractive index of a medium is 2.0, what is the maximum angle of incidence for total internal reflection when light travels to air?

Options:

  1. 30°
  2. 45°
  3. 60°
  4. 90°

Correct Answer: 60°

Solution: 

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.00/2.00) ≈ 30°; thus, maximum angle of incidence for total internal reflection is 60°.

If the refractive index of a medium is 2.0, what is the maximum angle of inciden

Practice Questions

Q1
If the refractive index of a medium is 2.0, what is the maximum angle of incidence for total internal reflection when light travels to air?
  1. 30°
  2. 45°
  3. 60°
  4. 90°

Questions & Step-by-Step Solutions

If the refractive index of a medium is 2.0, what is the maximum angle of incidence for total internal reflection when light travels to air?
  • Step 1: Understand that the refractive index (n) of a medium tells us how much light bends when it enters that medium. Here, n1 (the medium) is 2.0 and n2 (air) is 1.0.
  • Step 2: Recall that total internal reflection occurs when light travels from a denser medium (n1) to a less dense medium (n2).
  • Step 3: Use the formula for the critical angle (θc): θc = sin⁻¹(n2/n1). This formula helps us find the angle at which light will no longer pass into the second medium (air) but will instead reflect back into the first medium.
  • Step 4: Substitute the values into the formula: θc = sin⁻¹(1.00/2.00).
  • Step 5: Calculate the value: 1.00 divided by 2.00 equals 0.5. Now find sin⁻¹(0.5).
  • Step 6: The value of sin⁻¹(0.5) is 30°. This is the critical angle.
  • Step 7: The maximum angle of incidence for total internal reflection is 90° - θc. So, 90° - 30° = 60°.
  • Refractive Index – The refractive index is a measure of how much light slows down in a medium compared to its speed in a vacuum.
  • 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.
  • Critical Angle – The critical angle is the angle of incidence above which total internal reflection occurs, calculated using the refractive indices of the two media.
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