Optical systems are typically consist of multiple lenses and mirrors and are used in a wide variety of fields. While there exist a variety of setups, there are a few key concepts that are at the core of all of them. These could be used from the most advanced scientific research to a simple magnifying glass. They are also used in industry and consumer products such as glasses and cameras. We are going to go over these key concepts and show how they apply to telescopes, or more specifically rifle scopes. First, we will go over Snell\u27s Law of refraction as this is central idea governing almost all of the light interactions within the scope. Then we will apply this to simple one and two lens systems. Larger systems are more tedious to calculate, so we will then go over how to make calculations using matrices. The last optical theories that we will discuss are aberration and reflections along a few experiments to demonstrate their effects. We will also go over bullet trajectory as one needs to be able to know the path of the projectile in order to know where do aim using the scope