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 (n = 1.33)?

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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 (n = 1.33)?

Solution: Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, sin(30) = 0.5, so 1 * 0.5 = 1.33 * sin(θ2). Solving gives θ2 ≈ 22.5 degrees.

Steps: 10

Step 1: Identify the given information. We have the angle of incidence (θ1) which is 30 degrees, the refractive index of air (n1) which is approximately 1, and the refractive index of water (n2) which is 1.33.
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 sin(30 degrees) into the equation: 1 * 0.5 = 1.33 * sin(θ2).
Step 6: This simplifies to: 0.5 = 1.33 * sin(θ2).
Step 7: To find sin(θ2), divide both sides by 1.33: sin(θ2) = 0.5 / 1.33.
Step 8: Calculate the value: sin(θ2) ≈ 0.3759.
Step 9: Use the inverse sine function to find θ2: θ2 = sin^(-1)(0.3759).
Step 10: Calculate θ2, which gives approximately 22.5 degrees.