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A beam of light in diamond (n=2.42) strikes the surface of water (n=1.33). What
A beam of light in diamond (n=2.42) strikes the surface of water (n=1.33). What is the critical angle for total internal reflection?
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Practice Questions
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Q1
A beam of light in diamond (n=2.42) strikes the surface of water (n=1.33). What is the critical angle for total internal reflection?
25.5°
30.0°
36.9°
42.0°
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Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.33/2.42) ≈ 36.9°.
Questions & Step-by-step Solutions
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Q
Q: A beam of light in diamond (n=2.42) strikes the surface of water (n=1.33). What is the critical angle for total internal reflection?
Solution:
Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.33/2.42) ≈ 36.9°.
Steps: 6
Show Steps
Step 1: Identify the refractive indices of the two materials. For diamond, n1 = 2.42 and for water, n2 = 1.33.
Step 2: Use the formula for critical angle, which is θc = sin⁻¹(n2/n1).
Step 3: Substitute the values into the formula: θc = sin⁻¹(1.33/2.42).
Step 4: Calculate the value of 1.33 divided by 2.42, which is approximately 0.549.
Step 5: Find the inverse sine (sin⁻¹) of 0.549 using a calculator, which gives approximately 36.9°.
Step 6: Conclude that the critical angle for total internal reflection is about 36.9°.
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