Critical Angle Calculator

Formula

To calculate the Critical Angle (\(\alpha_c\)):

\[ \alpha_c = \sin^{-1}\left(\frac{n2}{n1}\right) \]

Where:

\(\alpha_c\) is the critical angle
\(n1\) is the refractive index in medium 1
\(n2\) is the refractive index in medium 2

What is a Critical Angle?

A critical angle is an angle described by Snell's law that is a measure of the refraction of light through different mediums. It is the angle of incidence above which total internal reflection occurs.

Example Calculation 1

Let's assume the following values:

Refractive Index in Medium 1 (n1) = 1.5
Refractive Index in Medium 2 (n2) = 1.0

Using the formula:

\[ \alpha_c = \sin^{-1}\left(\frac{1.0}{1.5}\right) = 41.81 \text{ degrees} \]

The Critical Angle is 41.81 degrees.

Example Calculation 2

Let's assume the following values:

Refractive Index in Medium 1 (n1) = 2.0
Refractive Index in Medium 2 (n2) = 1.33

Using the formula:

\[ \alpha_c = \sin^{-1}\left(\frac{1.33}{2.0}\right) = 41.14 \text{ degrees} \]

The Critical Angle is 41.14 degrees.