If the angle of incidence is 30° in a medium with a refractive index of 1.5, what is the angle of refraction in air?
Practice Questions
1 question
Q1
If the angle of incidence is 30° in a medium with a refractive index of 1.5, what is the angle of refraction in air?
19.5°
20.0°
22.5°
25.0°
Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1.5, n2 = 1.0, and θ1 = 30°. Thus, sin(θ2) = (1.5 * sin(30°))/1.0 = 0.75, leading to θ2 ≈ 48.6°.
Questions & Step-by-step Solutions
1 item
Q
Q: If the angle of incidence is 30° in a medium with a refractive index of 1.5, what is the angle of refraction in air?
Solution: Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1.5, n2 = 1.0, and θ1 = 30°. Thus, sin(θ2) = (1.5 * sin(30°))/1.0 = 0.75, leading to θ2 ≈ 48.6°.
Steps: 8
Step 1: Identify the given values. The angle of incidence (θ1) is 30°, the refractive index of the first medium (n1) is 1.5, and the refractive index of air (n2) is 1.0.
Step 2: Write down Snell's law formula: n1 * sin(θ1) = n2 * sin(θ2).
Step 3: Substitute the known values into the formula: 1.5 * sin(30°) = 1.0 * sin(θ2).
Step 4: Calculate sin(30°). It equals 0.5.
Step 5: Now substitute sin(30°) into the equation: 1.5 * 0.5 = 1.0 * sin(θ2).
Step 6: Simplify the left side: 0.75 = sin(θ2).
Step 7: To find θ2, use the inverse sine function: θ2 = sin⁻¹(0.75).
Step 8: Calculate θ2 using a calculator: θ2 ≈ 48.6°.
