Snell's Law

The Snell's Law calculator allows you to find any of the four unknowns involved in the formula for calculating the angle of refraction of light passing from one medium to another with a different refractive index.

All you have to do is select one of the following variables in the calculator in the Snell's Law:

  • n1: refractive index of first medium
  • n2: refractive index of the second medium
  • Angle of incidence (written in degrees)
  • Angle of refracted beam (also in degrees)

When you have selected the variable, fill in the values of the rest of the unknowns and press the calculate button to get the result. If you have the angles of incidence or refraction in radians, here you can to grades

Snell's Law Formula

Snell's law and refraction

The Snell's Law formula is as follows:

n1 seni = n2 senr

Where i and r are the angle of incidence and the refracted angle respectively.

Demonstration of Snell's Law


To know the demonstration of the Snell's Law formula we must first know the laws of refraction:

  1. The incident ray, the normal to the surface at the point of incidence and the refracted ray are in the same plane.
  2. The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant that is equivalent to the ratio of the respective velocities of propagation of the wave motion. This can be expressed mathematically by the following formula:

seni/senr = v1/v2

Once we know the laws of refraction by which Snell's Law is governed, we can move on to the subject of refraction. relative refractive index. This concept is the quotient of dividing the refractive indices of the media.

For example, the relative refractive index of medium 2 with respect to medium 1 is this:

n21 = n2 / n1

While the relative refractive index of medium 1 with respect to medium 2 would be this one:

n12 = n1 / n2

If we relate the formula of the relative refractive index to the second law of refraction, we have that:

n21 = n2 / n1 = v1 / v2 = seni / senr

From there, the expression of Snell's Law is deduced, and its formula is demonstrated:

n1 seni = n2 senr

Refractive index

We have spoken on several occasions about the refractive index But what exactly is it? The refractive index is a number that tells us the relationship between the speed of light in a vacuum (c) and the speed (v) of propagation in that medium. This can be expressed mathematically with the following formula:

n = c/v

In vacuum or air, the index of refraction is equal to 1. In all other media, n is greater than one since the speed of light (c) will always be greater than the speed of propagation in that medium.

Boundary angle and total reflection

Total reflection

There is a phenomenon called total reflection and it occurs when theLight passes from one medium to another with a lower refractive index.resulting in refraction away from the normal.

As we increase the angle of incidence, the refracted angle also increases until a point is reached at which the refracted angle increases, the light is totally reflected and the phenomenon of total reflection occurs.

In order to know what is the point from which the total reflectionIn this case, a limit angle is established in which the angle of refraction is equal to 90º. This is the formula to know what is the limit angle (L):

sinL = n2/n1

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