1. What is the Angle of Refraction Formula?

The Angle of Refraction Formula, derived from Snell's Law, calculates how much a light ray bends when passing from one medium to another with different refractive indices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Angle of refraction (degrees)
• \( n_1 \) — Refractive index of first medium
• \( n_2 \) — Refractive index of second medium
• \( i \) — Angle of incidence (degrees)

Explanation: The formula shows how light bends toward the normal when entering a denser medium (n₂ > n₁) and away from the normal when entering a less dense medium (n₂ < n₁).

3. Importance of Angle of Refraction

Details: Understanding refraction is crucial for lens design, fiber optics, prism operation, and many optical instruments. It explains phenomena like why objects appear bent in water.

4. Using the Calculator

Tips: Enter refractive indices (n₁ and n₂) as positive numbers. Angle of incidence must be between 0-90 degrees. Note that for n₁ > n₂ and large incidence angles, total internal reflection may occur.

5. Frequently Asked Questions (FAQ)

Q1: What are typical refractive index values?
A: Air ≈ 1.0003, Water ≈ 1.33, Glass ≈ 1.5-1.9, Diamond ≈ 2.42.

Q2: What happens at the critical angle?
A: When angle of refraction would be 90°, total internal reflection occurs for angles greater than the critical angle.

Q3: Does this work for all light wavelengths?
A: Refractive indices vary slightly with wavelength (dispersion), so calculations are wavelength-specific.

Q4: What if I get "NaN" as a result?
A: This means the calculation is invalid, usually because (n₁/n₂)sin(i) > 1, indicating total internal reflection.

Q5: Can this be used for sound waves?
A: Yes, the same principle applies to any wave phenomenon crossing a boundary between media with different propagation speeds.