A diamond has a refractive index of 2.42. What is the critical angle for total i

A diamond has a refractive index of 2.42. What is the critical angle for total internal reflection at the diamond-air interface?

A diamond has a refractive index of 2.42. What is the critical angle for total internal reflection at the diamond-air interface?

Step 1: Understand that the critical angle is the angle of incidence above which total internal reflection occurs.
Step 2: Know the formula for calculating the critical angle (θc) is θc = sin^(-1)(1/n), where n is the refractive index.
Step 3: Identify the refractive index of diamond, which is given as 2.42.
Step 4: Substitute the refractive index into the formula: θc = sin^(-1)(1/2.42).
Step 5: Calculate 1/2.42, which is approximately 0.4132.
Step 6: Use a calculator to find the inverse sine (sin^(-1)) of 0.4132.
Step 7: The result from the calculator will give you the critical angle, which is approximately 24.4°.

Refractive Index – The refractive index is a measure of how much light slows down when entering a material compared to its speed in a vacuum.
Total Internal Reflection – Total internal reflection occurs when light attempts to move from a denser medium to a less dense medium at an angle greater than the critical angle.
Critical Angle – The critical angle is the angle of incidence above which total internal reflection occurs, calculated using the refractive indices of the two media.