If the refractive index of a medium is 2.0, what is the critical angle for total internal reflection at the interface with air?
Practice Questions
1 question
Q1
If the refractive index of a medium is 2.0, what is the critical angle for total internal reflection at the interface with air?
30°
45°
60°
90°
Using the formula sin(θc) = n2/n1, we have sin(θc) = 1.00/2.00, leading to θc ≈ 30°.
Questions & Step-by-step Solutions
1 item
Q
Q: If the refractive index of a medium is 2.0, what is the critical angle for total internal reflection at the interface with air?
Solution: Using the formula sin(θc) = n2/n1, we have sin(θc) = 1.00/2.00, leading to θc ≈ 30°.
Steps: 6
Step 1: Understand the refractive index. The refractive index (n) of a medium tells us how much light bends when it enters that medium. Here, n = 2.0 for the medium.
Step 2: Identify the refractive index of air. The refractive index of air is approximately 1.0.
Step 3: Use the formula for critical angle. The formula to find the critical angle (θc) is sin(θc) = n2/n1, where n1 is the refractive index of the medium (2.0) and n2 is the refractive index of air (1.0).
Step 4: Substitute the values into the formula. We have sin(θc) = 1.0 / 2.0.
Step 5: Calculate the value. This simplifies to sin(θc) = 0.5.
Step 6: Find the critical angle. To find θc, we need to take the inverse sine (arcsin) of 0.5. This gives us θc ≈ 30°.
