If a light ray in diamond (n=2.42) strikes the diamond-air interface at an angle of 70°, will it undergo total internal reflection?

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Q: If a light ray in diamond (n=2.42) strikes the diamond-air interface at an angle of 70°, will it undergo total internal reflection?

Solution: The critical angle for diamond to air is sin⁻¹(1/2.42) ≈ 24.4°. Since 70° > 24.4°, total internal reflection will occur.

Steps: 7

Step 1: Understand that total internal reflection happens when light travels from a denser medium (like diamond) to a less dense medium (like air).
Step 2: Identify the refractive index of diamond, which is n = 2.42.
Step 3: Calculate the critical angle using the formula: critical angle = sin⁻¹(1/n).
Step 4: Substitute the value of n: critical angle = sin⁻¹(1/2.42).
Step 5: Calculate sin⁻¹(1/2.42) to find the critical angle, which is approximately 24.4°.
Step 6: Compare the angle of incidence (70°) with the critical angle (24.4°).
Step 7: Since 70° is greater than 24.4°, conclude that total internal reflection will occur.