Detailed Summary
When light travels from a denser medium to a rarer medium, it continues to refract according to Snell's law but bends away from the normal. As light moves from medium 1 (with speed v1) to medium 2 (with speed v2 where v2 > v1), this bending away is associated with an increase in the angle of refraction (r) compared to the angle of incidence (i).
The relationship governing this behavior is given by Snell's law:
$$ n_1 \sin(i) = n_2 \sin(r) $$
where $n_1$ and $n_2$ are the refractive indices of the two media, defined as \( n = \frac{c}{v} \), with \( c \) being the speed of light in vacuum.
As the angle of incidence approaches a critical angle ($i_c$), defined by the condition where $r = 90^ ext{o}$, the refracted light will no longer exist for incidences exceeding this angle. Instead, total internal reflection occurs. Thus, for angles of incidence greater than the critical angle, light is completely reflected back into the denser medium, a principle utilized in optical fibers and other applications. The refractive index and the critical angle are essential in determining the behavior of light in different media.