We have specifically avoided providing many mathematical equations in order to force the student to carefully observe the phenomenon and extract the general rules of such in words. However, given the mathematical experience of the typical student, it would be extremely difficult to arrive at Snell's law through any kind of natural process. More importantly, the mathematical construct of Snell's law is not required for understanding image formation if the student can put the phenomenon into words. Conversely, the student doesn't necessarily understand image formation simply by knowing the mathematical equation for Snell's law. This distinction between knowing the relevant mathematical equations and actually understanding what they mean is one of the key differences between learning about science and learning science.
Mathematical equations provide quantitative predictive ability.
Both of the above points need to be made explicitly to introductory students who often don't make these connections on their own. Our optics curriculum is developed to allow students to arrive at an understanding of the concepts mentioned above through a series of connected experiments in which the students make all the observations necessary internalize the concepts. This is in strong opposition to the more typical teaching method of discussing the phenomenon in lectures, providing equations derived or discovered by others in the past and then performing experiments which verify the lecture and equations. As this course has a primary goal the desire to teach students how to do science, the latter method is not appropriate. Hence, as in other portions of the curriculum, optics serves an excellent framework to teach science.