1. What is the Critical Angle Formula?

Definition: This calculator determines the critical angle for total internal reflection based on the refractive index of a medium.

Purpose: It helps in optics to determine the minimum angle of incidence beyond which light is totally reflected at a boundary between two media.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta_c \) — Critical angle (degrees)
• \( n \) — Refractive index of the medium (dimensionless)

Explanation: The critical angle is calculated by taking the inverse sine (arcsine) of the reciprocal of the refractive index.

3. Importance of Critical Angle Calculation

Details: Critical angle is crucial in fiber optics, prism design, and understanding light behavior at material boundaries.

4. Using the Calculator

Tips: Enter the refractive index (must be ≥ 1). The calculator will output the critical angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is total internal reflection?
A: It's the phenomenon where light is completely reflected at a boundary when the angle of incidence exceeds the critical angle.

Q2: What's a typical refractive index value?
A: For water it's about 1.33, glass 1.5-1.7, diamond 2.42. The refractive index must be ≥ 1.

Q3: Why must the refractive index be ≥ 1?
A: Because the sine function has a maximum value of 1, and n < 1 would make 1/n > 1 which is mathematically invalid.

Q4: What happens at the critical angle?
A: At exactly the critical angle, the refracted ray travels along the boundary between the two media.

Q5: How is this used in fiber optics?
A: Fiber optics rely on total internal reflection to keep light signals contained within the fiber core.