The mechanics of vibrations and waves are complex and important enough to demand their own course of study, whereas Optics is the branch of physics that studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it, these topics are important to know: Simple harmonic motion, the force oscillator, coupled oscillations, transverse wave motion, longitudinal waves, electromagnetic waves, optics; fraction and reflection, lenses and mirrors, the telescope and the microscope, introduction to wave propagation, Huijgens’ principle of wave superposition, wave fronts, and caustics.

Here I recommend studying The Physics of Vibrations and Waves by H. John Pain, and Optics by Eugene Hecht. 

By this point, you should have finished the introductory calculus books and are ready to move on to more advanced mathematics. You should start working through linear algebra, complex analysis, real analysis, partial differential equations, and ordinary differential equations (See Page of Mathematical Methods in Physics)