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What is the critical angle for total internal reflection from water to air (n_wa
What is the critical angle for total internal reflection from water to air (n_water = 1.33, n_air = 1.00)?
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Practice Questions
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Q1
What is the critical angle for total internal reflection from water to air (n_water = 1.33, n_air = 1.00)?
48.6 degrees
90 degrees
42.0 degrees
60 degrees
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The critical angle θ_c can be calculated using sin(θ_c) = n2/n1 = 1.00/1.33, which gives θ_c ≈ 48.6 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the critical angle for total internal reflection from water to air (n_water = 1.33, n_air = 1.00)?
Solution:
The critical angle θ_c can be calculated using sin(θ_c) = n2/n1 = 1.00/1.33, which gives θ_c ≈ 48.6 degrees.
Steps: 7
Show Steps
Step 1: Understand that the critical angle is the angle of incidence above which total internal reflection occurs.
Step 2: Identify the refractive indices: n_water = 1.33 and n_air = 1.00.
Step 3: Use the formula for the critical angle: sin(θ_c) = n2/n1, where n2 is the refractive index of air and n1 is the refractive index of water.
Step 4: Substitute the values into the formula: sin(θ_c) = 1.00 / 1.33.
Step 5: Calculate the value: sin(θ_c) ≈ 0.7519.
Step 6: Use the inverse sine function to find θ_c: θ_c = sin^(-1)(0.7519).
Step 7: Calculate θ_c, which is approximately 48.6 degrees.
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