Refraction is the bending of the path of a light wave as it passes across the boundary separating two media. Refraction is caused by the change in speed experienced by a wave when it changes medium. In Lesson 1, we learned that if a light wave passes from a medium in which it travels slow (relatively speaking) into a medium in which it travels fast, then the light wave would refract away from the normal. In such a case, the refracted ray will be farther from the normal line than the incident ray; this is the SFA rule of refraction. On the other hand, if a light wave passes from a medium in which it travels fast (relatively speaking) into a medium in which it travels slow, then the light wave will refract towards the normal. In such a case, the refracted ray will be closer to the normal line than the incident ray is; this is the FST rule of refraction. These two rules regarding the refraction of light only indicate the direction that a light ray bends; they do not indicate how much bending occurs. Lesson 1 focused on the topics of "What causes refraction?" and "Which direction does light refract?" Lesson 2 will focus on the question of "By how much does light refract when it crosses a boundary?"
The question is: "By how much does light refract when it crosses a boundary?" Perhaps there are numerous answers to such a question. (For example, "a lot," "a little," "like wow! Quite a bit dude," etc.) The concern of this lesson is to express the amount of refraction of a light ray in terms of a measurable quantity that has a mathematical value. The diagram to the right shows a light ray undergoing refraction as it passes from air into water. As mentioned in Lesson 1, the incident ray is a ray (drawn perpendicular to the wavefronts) that shows the direction that light travels as it approaches the boundary. (The meaning of an incident ray was first introduced in the discussion of Reflection of Light in Unit 13 of The Physics Classroom Tutorial.) Similarly, the refracted ray is a ray (drawn perpendicular to the wavefronts) that shows the direction that light travels after it has crossed over the boundary. In the diagram, a normal line is drawn to the surface at the point of incidence. This line is always drawn perpendicular to the boundary. The angle that the incident ray makes with the normal line is referred to as the angle of incidence. Similarly, the angle that the refracted ray makes with the normal line is referred to as the angle of refraction. The angle of incidence and angle of refraction are denoted by the following symbols