Snell's Law Calculator

The Snell's Law:

This law states that:

“A relationship between the angle of refraction and incidence, when light is entering from one medium to another”

The angle of refraction depends upon the refractive index of a particular medium. Snell's law calculation describes the working mechanism of refraction of light in various media. The wavelength of the light is different in various media like vacuum, water, ice, and air. This is why the light bends towards or away from the normal of two medium boundaries. Snell's law calculator determines the refractive index of light on the basis of the speed of light in a certain medium. If the speed of light changes then the refraction angle also changes as it depends on the wavelength or the speed of light in a certain medium.

Snell's Law Equation:

The refraction angle depends on the wavelength of light in both media. The Snell's law equation is given as follows:

\[ n_1 \, \sin \theta_1 = n_2 \, \sin \theta_2 \]

Where:

• \(n_1, n_2\) = the refractive index of medium 1 and medium 2, respectively.
• \(\theta_1\) = angle of incidence
• \(\theta_2\) = angle of refraction

You can express Snell’s law in the following form:

\[ \frac{\sin i}{\sin r} = \mu \]

Here:

• \(i\) = angle of incidence
• \(r\) = angle of refraction
• \(\mu\) = ratio of the refractive index of two media

The Snell law calculator assists to determine the behavior of light when traveling from incident to refracted medium. The Snells law equation tells us the light's bending when entering from one medium like a vacuum to water.

Example:

Calculate the refractive index of a ray of light from air to water using Snell's law. The refractive index of air and water at 20°C are \(n_1 = 1.000293\) and \(n_2 = 1.333\), respectively. The angle of incidence is around \(30^\circ\) when entering from air to water.

Given:

• Refractive index of air: \(n_1 = 1.000293\)
• Refractive index of water: \(n_2 = 1.333\)
• Angle of incidence: \(\theta_2 = 30^\circ = 0.523599 \text{ rad}\)

Solution:

The Snell's law formula for refraction is:

\[ \theta_1 = \sin^{-1} \left( \frac{n_1 \, \sin \theta_2}{n_2} \right) \]

Substitute the given values into the equation:

\[ \theta_1 = \sin^{-1} \left( \frac{1.000293 \times \sin(0.523599)}{1.333} \right) \]

Calculate the refracted angle:

\[ \theta_1 \approx 22.037^\circ \]

The Snells law calculator describes the change in the path or the bending of light rays when entering from one medium to another.

Chart of Refractive Index of Various Mediums:

The Snell's law calculation of refraction of various media is given below:

Working of the Snell’s Law Calculator?

The method of using the Snells law calculator is given below:

Input:

• Enter the refraction index of the first and second medium
• Enter the angle of incidence
• Tap Calculate

Output:

• The refractive index of light
• The angle of incidence & refraction 

References:

From the source Wikipedia: Snell's law, History  From the source brilliant.org: The refraction, Snell law formula