The Crisis of Prism Derivative

Lately,  I'm having a crisis that I called a "Prism Derivative Crisis". Which is about the derivative of the prism. It's stressful and challenging. Yes, and it's an assignment under the Vibrations, Waves & Optics (VWO) course. More specifically, Optics. I can think that this is just an introduction. I'm sure I will be facing the worst(i mean hard) questions that can probably be asked. For Year 2, there is a course just for Optics. I'm not saying that this subject is not interesting and really difficult. If another student is able to do it, then I actually can too. It just consists of hardworking, struggle, and understanding.

I'm thinking that I was having a hard time working on this derivative because of a lack of knowledge. That's my problem.

And to solve my problem is to keep learning and failing(then I can learn from mistakes too). The figure below is my work path in finding the derivative of the prism formula consisting of the refractive index, the angle of incidence, and the angle of deviation. \(\phi_o\) is used to denote the angle of deviation and \(\phi_i\) is denoted as the angle of incident and \(n\) is simply the index of refraction.

I have already contacted my VWO lecturer and actually, both of my derivatives were correct. Yeah, wow very glad. The only problem is that if my derivative is correct which must be correct as it is precise, then I will be able to find any unknown values. Such as I got the angle of incident and angle of deviation. Then I should be able to find the index of refraction, but I don't. I do actually find the n which is 1.55 as I remembered. But the scheme index was 1.33. When it contains the complex derivation of a formula, sometimes you can't just use Mathematica or else an intelligent machine. They sometimes calculate in a complex way which actually can be done easily.

I was still not sure if my calculation arrangement of the formula was correct (for the 1.55) [Just checked that it must be correct! I obey all the trigonometry rules), but I do find another way of it and finally, I do find the answer.

- hh