# How important is optics?

1. Dec 11, 2012

### phosgene

So I've just discovered that second year optics is entirely optional for physics majors (and we don't have to take it in third year, either). Since I'm mostly interested in atoms and how their interactions can explain the properties of bulk matter, is optics worth taking? It's my worst and most-hated subject. However, on the other hand, I understand that optics is pretty big in phyiscs, and I'd feel strange if I got my degree without doing much of it at all. I really just want to know if skipping optics would be detrimental for me later on.

2. Dec 11, 2012

### Staff: Mentor

Optics like lenses, mirrors and so on? While I think this is quite basic (and easy to learn, if necessary), there are many areas in physics where you never need that.
Light and its interaction in matter with relation to quantum mechanics? This looks more important for solid-state physics.

3. Dec 11, 2012

### dydxforsn

Third year optics is basically geometric optics (thin/thick lenses), basic wave mechanics, the derivation of the wave nature of light (Maxwell's equations to develop the wave equation and observance of plane wave solutions in free space, then some basic discussion of what happens when waves hit dielectric boundaries (reflection and refraction), etc.), the polarization of light, interference, diffraction, application of wave mechanics to the original lens situation (diffraction limited lens), probably Fourier transforms and their use in the mathematics of diffraction, and some more nuance topics depending on professors (waves in transmission lines, holography, lasers, etc.)

I will go through each of these topics individually, their relevance to other undergraduate physics courses (especially condensed matter which I am going to make the assumption that you are specifically referring to solid state physics), their degree of treatment in optics versus other courses (so you know what you will be getting anyway without taking a specific optics course), and then finally I will make some general statements about the value of optics as a physics course for undergraduates. There is a "too long; didn't read" (tl;dr) at the end that also discusses my feelings towards the necessity of the subject for the undergraduate.

1. Geometric optics - This is certainly a topic exclusive to optics courses save what experience you may have from an introductory survey course (this is the study of light from a straight-line particle-like ray standpoint as it traverses lenses). Something physics majors should know and is useful (mainly in the course of experimental techniques), but don't lose sleep over this one. You can learn a lot of this on your own (though this is true about everything, geometric optics is not that difficult and is usually the beginnings of any optics book. Note, however, that this goes well beyond your thin lens equation (it's non-trivial) learned in survey courses by introducing more formal (probably) arguments such as Fermat's principle, thick lenses, ray tracing techniques (huge series of matrix multiplications), aberrations, etc.) Not very relevant in other courses, but every now and then you will see a lens used for a particular reason in an experiment or something.

2. Basic wave mechanics - The basic mathematics of waves and how they are treated in the context of electromagnetic waves. This is a definite overlap with many other courses you have/will have taken. Specifically quantum adresses waves, electromagnetism courses cover the same material in similar detail, introductory courses, etc. So you will get it anyway, but nevertheless this would be good practice! Obviously relevant for many fields of physics (the mathematics of waves is very present in solid state physics.)

3. The derivation of the wave nature of light - treated in electromagnetism.

4. Reflection and refraction - studies the wave treatment of reflection and refraction (amplitude loses of the waves at dielectric boundaries, polarization shifts at boundaries, etc.) You will get this in your electromagnetism course so again no loss just practice/familiarity.

The following 4 topics are really the beef of the course and the reason for taking it. You will certainly see thinks like polarization of light and interference of waves in other courses, but the subjects are treated in much more detail and are of main instead of secondary consideration like they usually appear in other courses (for example the interference in double slit interference in quantum mechanics isn't as important for that course as the idea behind the experiment! Though obviously it is necessary to understand it, there will not be much detail given to the mathematical basis to the interference patterns in quantum mechanics..)

5. Polarization - the exact direction and path of motion of the oscillations of the electric field in light. This topic will definitely be seen in and dealt with in electromagnetism and even other courses such as statistical mechanics (knowledge of the different polarizations of light go into calculations like the blackbody spectrum.) However, the optics course will go into much more detail. Circular, and elliptical polarizations, quater wave plates, Jones vectors, etc. Again, the basic knowledge here (though it's only the kind of knowledge that could also be found in an electrodynamics text) is useful for some of the calculations in solid state physics.

6. Interference - Along with diffraction, the most useful reasons to take the course. Although interference is also treated in many other courses, the treatment here is quite thorough and in detail unlike what you will experience in other courses. Typically otherwise unaddressed topics include looking at multi-slit interference, thin film interference, interferometry, etc. Very useful for other physics courses, but usually that which is useful is at least basically treated as forwards in the sections that the concepts appear in other courses. I would still say that the formal treatment is one of the reasons for taking this course.

7. Diffraction - Very thorough treatment of diffraction that is mostly untreated in other physics courses. What I consider to be the beef of the course, be prepared to analyze this funny spiral shape called the "cornu spiral" to evaluate some particularly nasty integrals called the "Fresnel integrals". As far as uses? Everything from why Blu-Ray DVDs
are better to the immensely useful solid state physics topic of x-ray diffraction. It is true, however, that like double slit interference, the single slit diffraction pattern is about the most prevalent diffraction game in town and the mathematical form of the diffraction pattern could just be given to you in other courses where it comes up. Also many of the equations that are extremely useful are very easy to derive and/or could just be given to you (Bragg's law for x-ray diffraction of crystals.)

8. Fourier transforms - Application to the theory of diffraction.

Nuance topics - Professor dependent so I won't say much about it. I will say that transmission lines (optical fibers) are treated in electrodynamics, holography is usually barely touched on by professors at the end of the semester, etc. Also it's very important to realize that this is all from my prospective of what I saw myself go through in undergraduate optics as well as other syllabi I've seen from other undergraduate optics classes at other universities. My university is a pretty standard one in Texas, though I believe we didn't quite do as much as other universities (that are good).

The big picture (also the tl;dr heh, I was going to erase a lot of what I wrote in the interest of not going in to too much detail that wasn't even well written but I said screw it I had already written it and who knows what might be useful to you): I would definitely say that this course is very useful. Experimental tools in particular are abundant in the field of optics (lenses, interferometry, interference/diffraction, lasers, etc.) However, I would say that it is something you could miss and shouldn't lose sleep over. Based on the length of this post you might have thought I was going to say that it is a must-take course, but really as long as you are very keen in your advanced undergraduate electrodynamics course when electromagnetic waves are discussed you are really only missing geometric optics (bleh, also easy to learn on your own), and advanced takes at polarization/interference/diffraction. The stuff that is useful for solid state is overwhelmingly the basic stuff that I wouldn't be too concerned about taking an actual course on. If you are really truly set on going into solid state physics I would say that your biggest focus should be on statistical mechanics and quantum mechanics. Electrodynamics is also quite useful. Optics? It takes its place as a nuance pedigree that will always help, never hurt, but the case of necessarily taking a full course is a hard one.

It took this course as my very first advanced undergraduate course, so I gained a lot from it. However if you are keen in your electrodynamics, and don't go into "damage control" mode in likely the second semester of the advanced electrodynamics course when many overlaps with an optics course are to be had, then this course might have a large superflous component. However, think on the bright side, this course could definitely serve as a GPA boost, but don't go overboard with that, it's still a legitimate physics course - don't expect it to be easy, it's only easy relative to courses like electrodynamics and mechanics imo.

Last edited: Dec 11, 2012
4. Dec 12, 2012

### phosgene

Thanks for the replies :) Given the overlap with other courses, I think I might as well just take it. It should give me some practice so that I don't have as hard a time understanding the optics components in other courses. Thanks again guys!

Edit: also, I had no idea that what I was interested in was called 'solid state physics'. You learn something new every day (at least I hope I do).

Last edited: Dec 12, 2012
5. Dec 16, 2012

### mynick

dydxforsn wrote a huuuge reply. :O
i might read it someday :P