What is the critical angle for total internal reflection in a medium with a refractive index of 1.5?
Practice Questions
1 question
Q1
What is the critical angle for total internal reflection in a medium with a refractive index of 1.5?
30 degrees
45 degrees
60 degrees
90 degrees
The critical angle (θc) can be calculated using sin(θc) = 1/n. For n = 1.5, sin(θc) = 1/1.5 = 2/3. Therefore, θc = sin^(-1)(2/3) which is approximately 41.81 degrees, closest to 45 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the critical angle for total internal reflection in a medium with a refractive index of 1.5?
Solution: The critical angle (θc) can be calculated using sin(θc) = 1/n. For n = 1.5, sin(θc) = 1/1.5 = 2/3. Therefore, θc = sin^(-1)(2/3) which is approximately 41.81 degrees, closest to 45 degrees.
Steps: 9
Step 1: Understand that the critical angle is the angle of incidence above which total internal reflection occurs.
Step 2: Know that the formula to find the critical angle (θc) is sin(θc) = 1/n, where n is the refractive index of the medium.
Step 3: Identify the refractive index given in the question, which is n = 1.5.
Step 4: Substitute the value of n into the formula: sin(θc) = 1/1.5.
Step 5: Calculate 1/1.5, which equals 2/3.
Step 6: Now, we have sin(θc) = 2/3.
Step 7: To find θc, use the inverse sine function: θc = sin^(-1)(2/3).
Step 8: Use a calculator to find sin^(-1)(2/3), which is approximately 41.81 degrees.
Step 9: Note that this value is closest to 45 degrees.
