Optics/Total internal reflection

Total internal reflection is a phenomenon that occurs when mediums travel from a more optically dense medium to a less optically dense one. When light travells from an optically dense medium to a less optically dense medium, the light refracts away from the normal. If the angle of incidence is gradually decrased, one will notice that at a certain point, the refracted ray deviates so far away from the normal that it reflects rather than refracts.

When light travells from any medium to another less optically dense medium, total internal reflection will occur at a certain angle of incidence. In this case, a ray of light is travelling from plexiglass to air.

One can calculate the exact angle of incidence total internal refraction will occur by using Snell's Law:

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

$n_1\sin {\theta }_1=n_2\sin 90^{\circ }$

$\sin {\theta }_1=\frac{n_2\sin 90^{\circ }}{n_1}$

${\theta }_1={\sin }^{-1}\left(\frac{n_2\sin 90^{\circ }}{n_1}\right)$

Therefore, total internal reflection will occur after the incident angle is greater than θ₁.

Another interesting aspect of total internal reflection is that if one observes the refracted ray as the incident ray is gradually increased, the refracted ray slowly becomes dimmer until it disappears completely.

How do I know that the reflected ray isn't just the refracted ray? The second law of reflection states that "the incident ray, the reflected ray, and the normal are coplanar." Therefore, the refracted ray must be in the second medium. If it is in the same medium that it originated from, then it is the reflected ray. The reflected angle is also the same as the incident angle, which agrees with the first law of reflection.