Lab 3: diffraction

In lab 3, you will verify the position and intensity of the maxima of a laser beam passed through a diffraction grating. How you do this is fairly open ended, though I will guide you along the way and have written up some suggestions and guidelines.

If it is not possible to finish this lab in one session, we can continue it at the start of lab 4, which will be closely related anyway.

Updated schedule

We've decided to push Exam II back another week, to 14 April. The rest of the semester looks like this:

31 Mar Lasers 1 (A)    Lab 3: diffraction (B)   
5 April Lasers 1 (B)    Lab 3: diffraction (A)   
7 April Lasers 2 (A)    Lab 4: interferometry (B)   
12 April Lasers 2 (B)    Lab 4: interferometry (A)  
14 April EXAM 2           
19 April Fiber optics (A)    Lab 5: optical devices (B)   
21 April Fiber optics (B)    Lab 5: optical devices (A)   
26 April Holography (A)    Lab 6: spectral composition of light (B)   
28 April Holography (A)    Lab 6: spectral composition of light (A)   

Long story short: one more week before the exam, and on Thursday group A has lecture and group B has a lab.

I'll update the google calendar soon.

Updated HW2 solutions

In grading HW2, I found that a few of you had clever solutions to problem 8 different than what I posted earlier. I've updated the solutions to include them.

HW5 solutions

HW 5 solutions are out. Let me know if you find any serious errors.

Thanks to Mr. Murray and Mr. Dykes for solving the bonus problem on #1a - I had actually not worked it out myself (I used Wolfram), so I incorporated your results in the solutions. And, thanks to Mr. Lukens for asking the question that made me remember to double my results for 1b ...

Bonus on HW 5

In going over problem 1 on homework 5, I asserted (via Wolfram Alpha) that solving the equation

$ n\lambda = d^\prime - d =  \sqrt{\left(x+h\right)^2 + R^2} - \sqrt{\left(x-h\right)^2 + R^2}$

for x resulted in

$x = n\lambda\sqrt{\frac{4R^2+4h^2-\lambda^2n^2}{16h^2-4\lambda^2n^2}} \label{eq:alpha}$

If you can prove this with pencil and paper, showing all your steps, I'll give you 50% bonus credit on question 1 of homework 5. Include your work and a note indicating that you'd like to be considered for the bonus credit.

sub-wavelength optical microscopy

Neat, neat stuff. Hopefully we can get in to some stuff like this toward the end of the semester.

Lab Reports

I am behind on grading lab reports (and everything else) you may have noticed. What I can say is that all the reports I've gotten so far have been excellent, and you have no need to worry. I doubt any of them is below a mid B, so keep doing what you're doing ...

Some guidelines on the expectations. For the ~60min labs we do, I would expect a report of ~5 pages including a reasonable number of figures. Length is not as critical as completeness: if you can be concise, that is not a problem. I'd expect the following sections, with weighting for grading noted:

Theory & motivation 30%
Methods & data 40%
Analysis, discussion, conclusions 20%
Presentation & style 10%

Theory and motivation means why are you doing this experiment (what will you try to learn), and how did you model/analyze your setup mathematically. Methods and data means describing what you did and reporting raw data with some estimation of uncertainty (even if the uncertainty is only noted qualitatively). Analysis, discussion, and conclusions means extracting interesting parameters from your data, comparing them with the model you proposed in the first section, and discussing the implications for the model you used (is it right, within what accuracy?). Style is just what it sounds like ... that's grammar, formatting, quality of writing, and the rest of it.

Basically, what you have been doing is fine so far. Hopefully this will help you write up the remaining experiments.

Last: lab reports are due at the end of the semester before the final examination period.

Tuesday's lecture

Tuesday, you will get your exams back. Based on how they went and a few other factors, tomorrow we'll spend most our time solving exam problems and going over the current homework problems. We'll not cover much new material (other than what is relevant to the homework), and move on to diffraction on Thursday.

Part of the reason I'm skipping over some of the chapter on interference is that most of the last half is just straightforward applications of what we did already - superimposing two sources in, say, a Michelson interferometer and figuring out the interference condition from the geometry. Ditto for antireflective coatings, for the most part. So, we'll not cover a lot of that material in class, it will be up to you to read about those applications on your own. All you really need beyond what we've covered is more geometry, and accounting for the refractive index changing at an interface.

The gist of this is that if you (a) feel fine about the exam, (b) have done the homework already, and (c) will actually read the chapter, you won't miss much tomorrow. Thursday we start diffraction, which is also really more of the same, modulo a semantic argument I will mock briefly. ;-)

Timely bit of history

Diffraction & Rowland.

Today

Just to be clear - we're having a lecture. The lab I speak of is a take-home experiment you do on your own (i.e., at home); I'll give you the parts for that today.

HW5 is out

Here you go. Due March 25, the end of the week after spring break. There are 10 questions in total: 8 problems, and two short take-home experiments in which you will investigate thin film interference.

The procedure for the experiments you can find here. You will need a plano-convex lens and two glass slides, which I will provide in Thursday's (10 March) lecture. If you are not at that lecture, arrange to meet me at another time to get your components. Of course, you may feel free to use any stray plano-convex lenses you have lying around; the longer the focal length the better. ;-)

The experiments are quite simple, and almost purely qualitative, but I think quite illustrative and a bit of fun. There are a lot more things that can be done beyond what is in the procedure, so be creative and see what you can figure out. Both of them together should take no more than an 30-60 min, depending on your level of curiosity.

UPDATE - if you'd rather pick up your components sooner, I'll be in my Bevill office until about 2:30 today.

UPDATE 2 - small typo in the figure in problem 1. The lateral distance should be "R" not "8m." The height is still 8m. File has been reposted with the same name.

This week's schedule

This week, we'll start chapter 9 on interference. That will consume both lectures this week, as well as the first one after Spring Break.

Tuesday, we'll cover most of 9.1-9.3 (general remarks on superposition, the double slit experiment, and a bit on antennas), though I will follow a slightly different (but equivalent) approach to that used in the text. The main idea is that I'll add a few bits the book doesn't cover, and vice-versa, so between the lecture & reading you should come out ahead. You'll also get some HW back ...

Thursday, the plan is to cover superposition of an array of sources along with various amplitude-splitting interferometers (e.g., Michelson, Fabry–Pérot; 9.4-6, mostly). After the break, we'll finish it up and go into some applications of interferometry (e.g., spectroscopy). After that, it is on to diffraction, which is really more of the same.

The exams may be graded by Thursday. Dr. Kung and I each made up several problems for the exam, and we are first each grading our own problems, then reviewing the whole thing for consistency. There will be partial credit, and we will be as gentle as we can ... based on the collective results of the exam, I may spend some time after the break reviewing if we think there are areas that warrant it.

Lastly, I will also post some more formal guidelines for lab reports soon. I've spoken to most of you informally about it, and the reports I've received so far have been very good - so keep doing what you're doing if you've already turned in a report or two.

Exam 1 is TOMORROW

Exam 1 is tomorrow, Thursday, March 2 during the normal class period. The rules are basically thus:

• You can bring in one sheet of normal 8.5x11in paper front & back, or two sheets using one side only on each. On this sheet can be anything you like - formulas, notes, etc.
• Exotic formulas required for specific problems will be provided.
• There will be 6 problems of equal weight, you choose any 5 to solve. You will not get more credit for doing all 6. You must pick the 5 you want graded.
• The exam covers everything we have done in lecture thusfar.

It won't be so bad. Keep in mind that we bother to write up notes on a particular subject, that stuff is probably important.