If the refractive index of diamond is 2.42, what is the critical angle for total internal reflection when light travels from diamond to air?

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Q: If the refractive index of diamond is 2.42, what is the critical angle for total internal reflection when light travels from diamond to air?

Solution: Using the formula sin(θc) = n2/n1, where n1 = 2.42 (diamond) and n2 = 1.00 (air), we find θc ≈ 24.4°.

Steps: 7

Step 1: Understand the problem. We need to find the critical angle for light moving from diamond to air.
Step 2: Know the refractive indices. The refractive index of diamond (n1) is 2.42 and for air (n2) it is 1.00.
Step 3: Use the formula for critical angle: sin(θc) = n2/n1.
Step 4: Substitute the values into the formula: sin(θc) = 1.00 / 2.42.
Step 5: Calculate the value: sin(θc) ≈ 0.4132.
Step 6: Find the critical angle θc by taking the inverse sine (arcsin) of 0.4132.
Step 7: Calculate θc ≈ 24.4°.