What is the refractive index of a medium if the critical angle for total interna

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Question: What is the refractive index of a medium if the critical angle for total internal reflection is 30°?

Options:

Correct Answer: 1.73

Solution:

Using the formula n = 1/sin(θc), where θc = 30°, we find n = 1/sin(30°) = 1/0.5 = 2.00.

What is the refractive index of a medium if the critical angle for total internal reflection is 30°?

What is the refractive index of a medium if the critical angle for total internal reflection is 30°?

Step 1: Understand that the critical angle (θc) is the angle of incidence above which total internal reflection occurs.
Step 2: Recall the formula for refractive index (n) in relation to the critical angle: n = 1/sin(θc).
Step 3: Identify the given critical angle, which is 30°.
Step 4: Calculate the sine of the critical angle: sin(30°) = 0.5.
Step 5: Substitute the value of sin(30°) into the formula: n = 1/sin(30°) = 1/0.5.
Step 6: Perform the division: 1 divided by 0.5 equals 2.00.
Step 7: Conclude that the refractive index of the medium is 2.00.

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