A light ray passes from diamond (n=2.42) to air. What is the critical angle?

A light ray passes from diamond (n=2.42) to air. What is the critical angle?

Step 1: Understand that the critical angle is the angle of incidence above which light cannot pass through the boundary and is instead reflected back into the denser medium.
Step 2: Identify the refractive indices of the two materials involved. Here, diamond has a refractive index (n1) of 2.42 and air has a refractive index (n2) of 1.00.
Step 3: Use the formula for the critical angle (θc): θc = sin⁻¹(n2/n1).
Step 4: Substitute the values into the formula: θc = sin⁻¹(1.00/2.42).
Step 5: Calculate the value: 1.00 divided by 2.42 equals approximately 0.4132.
Step 6: Find the inverse sine (sin⁻¹) of 0.4132 using a calculator or trigonometric table, which gives approximately 24.4°.
Step 7: Conclude that the critical angle for light passing from diamond to air is approximately 24.4°.

Refraction and Critical Angle – The critical angle is the angle of incidence above which total internal reflection occurs when light passes from a denser medium to a less dense medium.
Snell's Law – The relationship between the angles of incidence and refraction, which is used to derive the critical angle.