A ray of light passes from air into water at an angle of incidence of 30 degrees. What is the angle of refraction in water? (Refractive index of water = 1.33)
Practice Questions
1 question
Q1
A ray of light passes from air into water at an angle of incidence of 30 degrees. What is the angle of refraction in water? (Refractive index of water = 1.33)
22.5 degrees
30 degrees
40 degrees
20 degrees
Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2), we find θ2 = sin^(-1)(sin(30 degrees)/1.33) = 22.5 degrees.
Questions & Step-by-step Solutions
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Q
Q: A ray of light passes from air into water at an angle of incidence of 30 degrees. What is the angle of refraction in water? (Refractive index of water = 1.33)
Solution: Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2), we find θ2 = sin^(-1)(sin(30 degrees)/1.33) = 22.5 degrees.
Steps: 10
Step 1: Identify the given information. We have an angle of incidence (θ1) of 30 degrees and the refractive index of water (n2) as 1.33. The refractive index of air (n1) is approximately 1.
Step 2: Write down Snell's law formula: n1 * sin(θ1) = n2 * sin(θ2).
Step 3: Substitute the known values into the formula: 1 * sin(30 degrees) = 1.33 * sin(θ2).
Step 4: Calculate sin(30 degrees). We know that sin(30 degrees) = 0.5.
Step 5: Substitute this value into the equation: 1 * 0.5 = 1.33 * sin(θ2).
Step 6: Simplify the equation: 0.5 = 1.33 * sin(θ2).
Step 7: Solve for sin(θ2) by dividing both sides by 1.33: sin(θ2) = 0.5 / 1.33.
Step 8: Calculate the value: sin(θ2) ≈ 0.3759.
Step 9: Find θ2 by taking the inverse sine: θ2 = sin^(-1)(0.3759).
Step 10: Calculate θ2 to find the angle of refraction in water, which is approximately 22.5 degrees.
