Snells Law Calculator

What is Snell's Law?

Snell's Law describes how light changes direction as it passes from one medium to another. It states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media.

How to Use This Calculator

1. Enter the angle of incidence (θ₁) in degrees - this is the angle between the incoming light ray and the normal (perpendicular) to the surface.
2. Enter the refractive index of the first medium (n₁). For example, the refractive index of air is approximately 1.00.
3. Enter the refractive index of the second medium (n₂). For example, the refractive index of water is approximately 1.33.
4. Click the "Calculate" button to determine the angle of refraction (θ₂).

Understanding the Results

The calculator will display the angle of refraction in degrees. If total internal reflection occurs (when light travels from a medium with higher refractive index to one with lower refractive index at a steep angle), the calculator will indicate this instead of an angle.

Practical Applications

Snell's Law has numerous applications in optics, including:

• Designing lenses and optical instruments
• Understanding fiber optics and how light travels through them
• Explaining mirages and other optical illusions
• Calculating the critical angle for total internal reflection

Example

Imagine light traveling from air (n₁ = 1.00) into water (n₂ = 1.33) at an angle of 30 degrees to the normal. Using Snell's Law:

n₁ sin(θ₁) = n₂ sin(θ₂)
1.00 sin(30°) = 1.33 sin(θ₂)
sin(θ₂) = (1.00 × sin(30°)) / 1.33 ≈ 0.376
θ₂ ≈ 22.1°