In other words, it's the largest possible value of `theta_i` such that `theta_t = sin^(-1) (n_1/n_2 sin(theta_i) ) ` evaluates to an answer. Since `n_2 < n_1`, there an angle, called the Critical Angle 4, that is the largest incident angle that will still result in a transmitted wave. To see why, or at least when, this happens, let's look at Snell's Law rearranged to solve for `theta_t`. As the name suggests, TIR is when all of the incident is reflected, so no light transmits into the second material. If `n_2 < n_1`, there's an interesting phenomena termed Total Internal Reflection (TIR) 3. Both `theta_i` and `theta_t` are measured from the normal, but they're on opposite sides of the normal and interface. The Law of Refraction, commonly known as Snell's Law 2, is `n_1 sin(theta_i) = n_2 sin(theta_t)`. Both `theta_i` and `theta_r` are measured from the normal, but they're on opposite sides of the normal. As you can see, the angle of reflection is entirely independent of the indices of refraction of the two materials.

The Law of Reflection is fairly straightforward: `theta_i = theta_r` 1. The relationship can be seen in the following formula: Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction. The law is also satisfied in metamaterials, which allow light to be bent 'backward' at a negative angle of refraction with a negative refractive index. In optics, the law is used in ray tracing to compute the angles of incidence or transmission, and in experimental optics to find the refractive index of a material. Snell's law (also known as Snell-Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and transmission, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In the picture, the horizontal line is the normal, and the vertical line is the interface between the two materials (between blue and white). The 'normal' is a line perpendicular to the intersection of the two materials. The angles are measured from the normal (see picture). Material 2 (red in the picture), where the light's going, is on the right. The light is coming in from material 1 (blue in the picture) on the left. The equations are solved for the incident, reflected, and transmitted angles and the materials' indices of refraction at the interface between two materials. The Angles of Reflection and Refraction Calculator provides calculations for reflection and refraction.

Reflection calculator