Snell's Law Calculator

Understanding Snell's Law Calculator

Snell's Law describes how light bends when passing between media with different refractive indices. When the refracted angle reaches 90°, total internal reflection occurs.

How to use this calculator

1. Enter the refractive index of the first medium, \(n_1\).
2. Enter the incident angle, \(\theta_1\), in degrees or radians, matching the calculator setting.
3. Enter the refractive index of the second medium, \(n_2\).
4. Read the calculated refraction angle, \(\theta_2\), and compare it with the step-by-step result.

The formula explained

Snell's Law computes the angle of refraction, \(\theta_2\), from the incoming angle and the two refractive indices. It shows how the path of light changes when it crosses a boundary.

• \(n_1\) = refractive index of the first medium
• \(\theta_1\) = angle of incidence, measured from the normal
• \(n_2\) = refractive index of the second medium
• \(\theta_2\) = angle of refraction, measured from the normal

Step by step method

1. Start with \(n_1 \sin\theta_1 = n_2 \sin\theta_2\).
2. Rearrange to isolate \(\sin\theta_2\), so \(\sin\theta_2 = \frac{n_1 \sin\theta_1}{n_2}\).
3. Take the inverse sine to find \(\theta_2\), so \(\theta_2 = \sin^{-1}\!\left(\frac{n_1 \sin\theta_1}{n_2}\right)\).

Worked example

Problem. Light travels from air into water. If \(n_1 = 1.00\), \(\theta_1 = 30^\circ\), and \(n_2 = 1.33\), find the angle of refraction \(\theta_2\).

1. Use Snell's Law, \(1.00\sin(30^\circ) = 1.33\sin\theta_2\).
2. Compute \(\sin(30^\circ) = 0.5\), so \(\sin\theta_2 = \frac{1.00 \cdot 0.5}{1.33} \approx 0.3759\).
3. Take the inverse sine, \(\theta_2 \approx \sin^{-1}(0.3759) \approx 22.1^\circ\).

Tips and common mistakes

• Make sure the angle is measured from the normal, not from the surface.
• If \(\frac{n_1 \sin\theta_1}{n_2} > 1\), refraction is not possible and total internal reflection occurs.

Frequently asked questions