If the refractive index of a medium is 2.0, what is the maximum angle of incidence for total internal reflection when light travels to air?
Practice Questions
1 question
Q1
If the refractive index of a medium is 2.0, what is the maximum angle of incidence for total internal reflection when light travels to air?
30°
45°
60°
90°
Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.00/2.00) ≈ 30°; thus, maximum angle of incidence for total internal reflection is 60°.
Questions & Step-by-step Solutions
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Q
Q: If the refractive index of a medium is 2.0, what is the maximum angle of incidence for total internal reflection when light travels to air?
Solution: Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.00/2.00) ≈ 30°; thus, maximum angle of incidence for total internal reflection is 60°.
Steps: 7
Step 1: Understand that the refractive index (n) of a medium tells us how much light bends when it enters that medium. Here, n1 (the medium) is 2.0 and n2 (air) is 1.0.
Step 2: Recall that total internal reflection occurs when light travels from a denser medium (n1) to a less dense medium (n2).
Step 3: Use the formula for the critical angle (θc): θc = sin⁻¹(n2/n1). This formula helps us find the angle at which light will no longer pass into the second medium (air) but will instead reflect back into the first medium.
Step 4: Substitute the values into the formula: θc = sin⁻¹(1.00/2.00).
Step 5: Calculate the value: 1.00 divided by 2.00 equals 0.5. Now find sin⁻¹(0.5).
Step 6: The value of sin⁻¹(0.5) is 30°. This is the critical angle.
Step 7: The maximum angle of incidence for total internal reflection is 90° - θc. So, 90° - 30° = 60°.
