A ray of light passes from air into water. If the angle of incidence is 30 degrees, what is the angle of refraction?

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Q: A ray of light passes from air into water. If the angle of incidence is 30 degrees, what is the angle of refraction?

Solution: Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1 (air), n2 = 1.33 (water). Solving gives θ2 ≈ 22 degrees.

Steps: 12

Step 1: Identify the angle of incidence (θ1), which is given as 30 degrees.
Step 2: Identify the refractive index of air (n1), which is 1.
Step 3: Identify the refractive index of water (n2), which is approximately 1.33.
Step 4: Write down Snell's law formula: n1 * sin(θ1) = n2 * sin(θ2).
Step 5: Substitute the known values into the formula: 1 * sin(30 degrees) = 1.33 * sin(θ2).
Step 6: Calculate sin(30 degrees), which is 0.5.
Step 7: Now the equation looks like: 1 * 0.5 = 1.33 * sin(θ2).
Step 8: Simplify the equation: 0.5 = 1.33 * sin(θ2).
Step 9: Solve for sin(θ2) by dividing both sides by 1.33: sin(θ2) = 0.5 / 1.33.
Step 10: Calculate sin(θ2) to find its value, which is approximately 0.3759.
Step 11: Use the inverse sine function (arcsin) to find θ2: θ2 = arcsin(0.3759).
Step 12: Calculate θ2, which is approximately 22 degrees.