If the refractive index of a medium is 2.0, what is the critical angle for total

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Question: If the refractive index of a medium is 2.0, what is the critical angle for total internal reflection at the interface with air?

Options:

Correct Answer: 60°

Solution:

Using the formula sin(θc) = n2/n1, we have sin(θc) = 1.00/2.00, leading to θc ≈ 30°.

If the refractive index of a medium is 2.0, what is the critical angle for total internal reflection at the interface with air?

If the refractive index of a medium is 2.0, what is the critical angle for total internal reflection at the interface with air?

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°.

Refractive Index – The refractive index is a measure of how much light slows down in a medium compared to its speed in a vacuum.
Critical Angle – The critical angle is the angle of incidence above which total internal reflection occurs when light travels from a denser medium to a less dense medium.
Total Internal Reflection – Total internal reflection is the phenomenon that occurs when light hits the boundary of a medium at an angle greater than the critical angle, causing it to reflect entirely back into the medium.