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° when light travels to air?

Options:

Correct Answer: 1.73

Solution:

Using sin(30°) = 0.5, n = 1/sin(30°) = 1/0.5 = 2. Therefore, the refractive index is 2.

What is the refractive index of a medium if the critical angle for total internal reflection is 30° when light travels to air?

What is the refractive index of a medium if the critical angle for total internal reflection is 30° when light travels to air?

Step 1: Understand that the critical angle is the angle of incidence above which total internal reflection occurs.
Step 2: Recall the formula for the critical angle (θc) in terms of the refractive index (n): sin(θc) = 1/n.
Step 3: We know the critical angle (θc) is 30 degrees. So, we can write: sin(30°) = 1/n.
Step 4: Calculate sin(30°). It is equal to 0.5.
Step 5: Substitute sin(30°) into the equation: 0.5 = 1/n.
Step 6: Rearrange the equation to find n: n = 1/0.5.
Step 7: Calculate 1/0.5, which equals 2.
Step 8: Conclude that the refractive index of the medium is 2.

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