A light ray traveling in a medium with n=2.0 strikes a boundary with air at an angle of incidence of 45°. What will be the angle of refraction in air?

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22.5°
45°
60°
90°

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Q: A light ray traveling in a medium with n=2.0 strikes a boundary with air at an angle of incidence of 45°. What will be the angle of refraction in air?

Solution: Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 2.0, θ1 = 45°, and n2 = 1.0 (air). Thus, 2.0 * sin(45°) = 1.0 * sin(θ2) leads to sin(θ2) = √2, which gives θ2 = 90°.

Steps: 9

Step 1: Identify the refractive indices. The refractive index of the medium is n1 = 2.0 and for air, n2 = 1.0.
Step 2: Identify the angle of incidence. The angle of incidence θ1 is given as 45°.
Step 3: Write down Snell's law formula: n1 * sin(θ1) = n2 * sin(θ2).
Step 4: Substitute the known values into the formula: 2.0 * sin(45°) = 1.0 * sin(θ2).
Step 5: Calculate sin(45°). It is √2/2.
Step 6: Substitute sin(45°) into the equation: 2.0 * (√2/2) = 1.0 * sin(θ2).
Step 7: Simplify the left side: √2 = sin(θ2).
Step 8: Find the angle θ2 by taking the inverse sine: θ2 = sin⁻¹(√2).
Step 9: Recognize that sin(90°) = 1, so if sin(θ2) = √2, then θ2 = 90°.

A light ray traveling in a medium with n=2.0 strikes a boundary with air at an angle of incidence of 45°. What will be the angle of refraction in air?

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