Incident Angle using Snell's Law Calculator

Snell's Law Formula:

\[ \theta_i = \text{arcsinh}\left(\frac{n_2 \cdot \sin(\theta_r)}{n_1}\right) \]

Incident Angle (θᵢ):

radians

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Snell's Law?

Snell's Law describes the relationship between the angles of incidence and refraction when light passes through different media with different refractive indices. It helps determine how light bends when transitioning between materials.

2. How Does the Calculator Work?

The calculator uses the modified Snell's Law formula:

\[ \theta_i = \text{arcsinh}\left(\frac{n_2 \cdot \sin(\theta_r)}{n_1}\right) \]

Where:

\( \theta_i \) — Incident angle (radians)
\( n_2 \) — Refractive index of medium 2
\( \theta_r \) — Refracted angle (radians)
\( n_1 \) — Refractive index of medium 1

Explanation: This formula calculates the incident angle using hyperbolic sine function based on the refractive indices and refracted angle.

3. Importance of Incident Angle Calculation

Details: Calculating incident angle is crucial in optics for understanding light behavior at interfaces, designing optical systems, and analyzing light propagation through different media.

4. Using the Calculator

Tips: Enter refractive indices as positive values (n₂, n₁ > 0), refracted angle in radians (θᵣ ≥ 0). All values must be valid numerical inputs.

5. Frequently Asked Questions (FAQ)

Q1: Why use hyperbolic sine in this formula?
A: The hyperbolic sine function (arcsinh) is used to handle cases where the ratio exceeds the normal range of trigonometric functions, providing accurate results across wider input ranges.

Q2: What are typical refractive index values?
A: Air: ~1.0, Water: ~1.33, Glass: ~1.5-1.9, Diamond: ~2.42. Values vary based on material and wavelength.

Q3: When does total internal reflection occur?
A: Total internal reflection occurs when light travels from a higher to lower refractive index medium and the incident angle exceeds the critical angle.

Q4: Are there limitations to this calculation?
A: This calculation assumes ideal conditions and may not account for material dispersion, absorption, or other complex optical phenomena.

Q5: Can this be used for all light wavelengths?
A: Refractive indices vary with wavelength, so for precise calculations, wavelength-specific refractive index values should be used.