Applying Equations and Relationships to Solve Questions (Refraction Index, Snell’s Law, Critical Angle, Intensity of Light)

How do I apply the relationships below to make quantitative predictions?

In this post, we apply equations and relationships to solve problems and questions or make quantitative predictions in a variety of situations, as a part of the Prelim Physics course under the module Waves and Thermodynamics and sub-part Ray Model of Light. We apply the following relationships below to assist us.

$n_{x} = \frac{c}{v_{x}}$ for the refractive index of medium , is the speed of light in the medium.
$n_{1} sin \theta _{1} = n_{2} sin \theta _{2}$ Snell’s Law
$sin \theta _{c} = \frac{n_{2}}{n_{1}}$
$I_{1} r_{1} ^{2} = I_{2} r_{2} ^{2}$ to compare the intensity of light at two points, $r_{1}$ and $r_{2}$

The following three videos cover the range of relationships, and how to apply these to practice questions.