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A light ray traveling in diamond (n=2.42) strikes the diamond-air interface. Wha
A light ray traveling in diamond (n=2.42) strikes the diamond-air interface. What is the critical angle for total internal reflection?
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Practice Questions
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Q1
A light ray traveling in diamond (n=2.42) strikes the diamond-air interface. What is the critical angle for total internal reflection?
24.4°
30.0°
36.0°
42.0°
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Using Snell's law, sin(θc) = n2/n1 = 1.00/2.42. Thus, θc ≈ 24.4°.
Questions & Step-by-step Solutions
1 item
Q
Q: A light ray traveling in diamond (n=2.42) strikes the diamond-air interface. What is the critical angle for total internal reflection?
Solution:
Using Snell's law, sin(θc) = n2/n1 = 1.00/2.42. Thus, θc ≈ 24.4°.
Steps: 7
Show Steps
Step 1: Understand that we are looking for the critical angle (θc) for light traveling from diamond to air.
Step 2: Recall that the refractive index of diamond (n1) is 2.42 and the refractive index of air (n2) is approximately 1.00.
Step 3: Use Snell's law, which states that sin(θc) = n2/n1.
Step 4: Substitute the values into the equation: sin(θc) = 1.00 / 2.42.
Step 5: Calculate the value: sin(θc) ≈ 0.4132.
Step 6: Use the inverse sine function (arcsin) to find θc: θc ≈ arcsin(0.4132).
Step 7: Calculate θc to find that it is approximately 24.4°.
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