Everyday Optics: Cosmetic Mirror

Last week, while helping a friend study for the qualifying exam, I posed him this question--explain how a cosmetic mirror works.

For those of you who have never used one, a cosmetic mirror is a mirror that creates a magnified image. Usually they are small and hand held so you can use them to apply things like eye liner and see what you are doing.

I am embarrassed to say, while we had the right instincts in this matter, it took us a day to figure out how to do the ray tracing to prove we were right, so I figured I'd make a blog post out of it.

To start with, let's examine the three types of basic mirrors. There is the flat mirror, which is the kind that hangs over your bathroom sink and is the kind of mirror pretty much everyone is familiar with. It can not magnify, either positively (make it bigger) or negatively (make it smaller). So that one's out.

Don't you love my white board illustrations?

There is the convex mirror, which is bowed outward and is the kind you see in gas stations as a security measure. They create smaller, distorted images of whatever is in front of it. So that's out.

No? Too bad.

Lastly, there is the concave mirror, which bows inward. This is the  most complicated mirror, because what it does depends on what region you are in, as shown below.

I do need new markers though....

So this is the kind of mirror we need, and we know we need to be inside the focal point for this to work. That's fine, because you are usually holding this close to your face anyway. However, the image that it creates is imaginary, and that's the part that was tripping us up while we were drawing the ray diagram.

As you can see, to demonstrate the effect we know occurs, we need to trace partially real rays, and partially imaginary rays. The imaginary rays are what we perceive happens, the virtual image that is created 'in' the mirror.

Diagram a la Hecht

So there you have it. How a cosmetic mirror works. Incidentally, this also applies to the image created  in bowl of spoon. See if you can find the focal point!

~AMPH

Great is the mystery of the fridge

Life was weird today. But perhaps nothing quite so weird as my lunch missing from the break room fridge.

Now, I know that this sort of thing is not uncommon is some places, but you have to understand something about this particular fridge.

Nothing leaves this fridge.

When I came to the program, there was a three year old carton of eggnog in the fridge. It lived there for another year after I got there.

Chinese leftovers, hot pockets, soy sauce, this and much more have lived in that fridge for months without molestation.

I leave my yogurt in there overnight, one night, as I frequently do so I don't have to make a time-costly detour on teaching mornings, and it vanishes.

What gives?

Everyday Optics: Rearview Mirrors

I have been helping some friends study for the qualifying exam lately, and part of that has been coming up with problems for them to ponder and answer. As I've done this, I've realized just how much optical phenomena surround us everyday, and just how much of it can be treated in terms of simple geometrical optics. (Why I didn't discover this when I myself was studying is anyone's guess).

Take, for example, your rearview mirror. If you drive, you know this mirror is a good friend. And if you do a lot of night driving, you know that moving that little lever on the bottom forward means you don't have to be blinded by the headlights of the guy behind you. But you probably have not thought about why that works. You are just thankful it does when the idiot behind you has his brights on. 

The way that this works is simple, cool and demonstrates the usefulness of basic optics.

First, let's look at the case of the normal, daytime mirror. In this situation, it works like any other mirror. You have a piece of silvered glass (glass with a highly reflective material on one side) that is angled so that it directed light from objects directly behind the driver's right shoulder into the driver's eyes. 

Yes, I do illustrations on my whiteboard.

From an optical standpoint, there are two reflective surfaces or interfaces. Reflections occur wherever there is an index mismatch, and the stronger the mismatch, the stronger the reflection. How much reflection occurs can be found using the Fresnel Equations.  In the case of a rearview mirror, we have a air/glass and a glass/reflective coating interface. One other thing to note is that rearview mirrors are not like your bathroom mirror, which is made of planar glass. Rather, rearview mirrors are prismatic, which is to say if you cut one in half from top to bottom, you would notice that the glass is ever so slightly trapezoidal, like this:

This allows you to choose which reflection you want to use--the silvered surface reflection for daytime driving, where everything is the same brightness, thanks to sunlight.

Or the first glass surface at night, where you just want enough light to know someone is behind you, because you aren't going to get any kind of detail from the reflected image anyway. Notice that the light still is reflecting off the silvered surface, but now it is being reflected at the ceiling. In fact, if you accidentally leave it in the night position during the day, you'll notice a very faint reflection of what's behind you, and a much stronger reflection of your car ceiling.

Behold! PhysicsGal in her minivan, parked safely in her garage.

Alright, I admit it. Geometrical optics is kinda cool and useful. Only took me...6 years to figure that out? I think I'm ashamed of myself. 

Puzzles are a lot like research

Recently I decided Dear Husband and I should take up jigsaw puzzles. It's a good hobby. It's relatively inexpensive, time consuming, can be done together, and it yields pretty pictures when its all done. Actually, its mostly the latter.

Our house has a lot of big, blank walls painted a cream color. Some have holes from where the previous owner hung pictures. We did not come to the house with a lot of pictures, and we are too frugal to buy real paintings. We could buy reproductions, but even those are somewhat pricey and it feels cheap to us.

 So until we can afford/find/agree on original art, jigsaw puzzles seem to be a good compromise. They are obviously reproductions. They are cheap. And, again, they provide hours of entertainment.

There are many ways of going about completing puzzles with lots of little pieces. There is the "Find all the Edge Pieces" method, which finds the borders and works its way inward. There is the "Hunt and Peck" method, seemingly preferred by my husband which starts with just putting together any pieces that fit. My method could be called "Divide and Conquer" or "Painstaking", which involves dividing up the pieces by come features (color and/or pattern) and focusing on getting all those pieces together. It involves choosing a piece, and trying every other piece to go with that piece until you have built up that entire section.

It is very slow going at first, but as you build up the sections you can begin to eliminate pieces from consideration on the ground of them not being the right shape, being too long, too short. Is it the fastest method? Maybe not. But it involves a lot less trying the same piece in the same spot over and over.

As I went, I realize that this is the same way I attack research (and most of my problems). Slowly and methodically. I think it confuses my PI sometimes why I insist on keeping constants, for example, running around and doing things piece by piece instead of lumping things together cleverly. I don't do clever lumping. My brain doesn't work like that.

It takes me time to get going. I am not fast at the outset. But I get faster and faster as I go because I can see pattern emerge specifically because I didn't lump things at the outset.

It's kind of nice for me to realize that I do have internal consistency in this. And it's nice to see the (more) tangible result of my methods in puzzles, even when the research is slower than molasses in January.

Shrove Tuesday

Today is Shrove Tuesday. You may know it better as Mardi Gras, or "Fat Tuesday". It marks the last day in the season after Epiphany and the last day before the season of Lent. For people who are not Christian, or who do not observe the liturgical year, it's excuse to party on a Tuesday, or party all week long depending on where you live.

If you are liturgical and you do observe Lent in an actual time of reflection and repentance kind of way, not just in the I-can't-eat-this-today kind of way, Shrove Tuesday is a day to prepare both spiritually and potentially physically for Lent. The 'shrove' part of the name comes from the fact that people used to do a pre-Lent confession as part of their preparations.

For me this involved getting rid of or hiding a lot of the sweets in my house, and putting all the alcohol away. Our assistant Rector has inviting the parish to join in a kind of fast this Lent, focusing on our relationship to food and how it can help or hurt our relationship to others and to God.  The idea is to eat simply, rather than focusing on giving up specific things for specific days or trying to not eat at all.

My relationship to food is complicated. It's a hobby, a necessity, an indulgence, a comfort, a source of pride and a means of love. I'm going to be trying to use this Lent to try and weed out some of my more selfish motives around food, and try to refocus on the ways God provides for me, and on using my skills to benefit others, not just myself.

If you are planning on observing some sort of fast this Lent, whether of food, entertainment or something else, I hope it helps you draw closer to our Lord and Savior. If not, enjoy all the extra ice cream.

What is color?

This year's Flame Challenge was to explain what color is. Never heard of the Flame Challenge? It's a really cool contest started three years ago by the Alan Alda Center for Communicating Science. Yes, Alan Alda from M*A*S*H the tv show. The contest asks scientists to explain, at the level of an 11-year-old but without oversimplifying, a basic question. The first year asked "What is flame?" and the second year asked "What is time?". I really recommend you go watch the winning videos--they are awesome.

I would have loved to enter the contest this year, but learned about it too late. The written entry had a word limit of 300 (WAY too short), while the video had a 6 minute limit (into which you can cram more like 1000 words). Next year, I'm going to look for it early so I can actually through together a video.

But I thought there was no reason to do a blog post on the topic!

What is color? Well, that kinda depends on whether you are talking about colored light or a colored object. Because while the answers are similar, they aren't the same. Let's start with what makes colored light, and an analogy!

You've all seen (and probably been forced to learn at some point) a musical instrument. I learned to play clarinet at an earlier point in my life, so I'll use that for this analogy. You know that if you hold certain keys down and blow into the clarinet  (thus vibrating the column of air in said instrument) you get a certain note. If you hold down different keys, you'll get a different note. But unless your clarinet is WILDLY out of tune, you will never ever get a middle C out of the soprano F fingering. What's happening is that by holding some holes open and others closed you are causing the column of air to vibrate at a different frequency, which we perceive as musical notes.

While sound is vibrations in air, light is vibrations in  the electromagnetic field created by electrons jumping around in an atom. It works like this. All atoms have distinct energy levels that their electrons are allowed to inhabit. The electrons are not allowed to be any where but those energy levels.

You may  be on any level you have the energy to reach, but never anywhere in between

Normally, electrons exist in their ground state, or lowest energy level. To get to the next level, they need an extra kick of energy.

Once they are up there though, they can't stay for long. Very few of the non-ground state energy levels are stable, so the electron only gets to hang out a short while before it needs to fall back to the ground state. Only problem is it can't exist in the ground state with this extra energy, which it conveniently gives off as a photon, or a burst of vibrations, in the electromagnetic field. How much energy it needs to give off, which is determined by how far it needs to 'fall', tells you at what frequency it vibrates. Each frequency has its own color attached to it. So if you only have one type of atom, you are only going to be able to get a few colors, or spectral lines.Your eyes don't see them as individual lines, but as a blended single color, just like your ears don't hear individual notes in a chord.

How an non-light-source object  has a color is different. Lets imagine we have a light bulb that gives off white light. That is, it has electrons giving off photons of many different wavelengths across the whole spectrum, which we perceive as white. You could think of this like an orchestra warming up. You just hear a cacophony of noise; to our eyes, a 'cacophony' of light looks white. Then that light strikes an object--lets say a red brick fireplace. All the photons of every color imaginable strike the brick. All the photons that are purple, indigo, blue, green, yellow and orange get absorbed by the atoms in the brick. They cause the atoms to vibrate and if you shone enough light on the brick for long enough, the bricks would get hot (think about a brick patio in the summer time). The red photons don't get absorbed though. They aren't the right frequency to be absorbed, so they get spat out in all directions. The photons that happen to get spat out in the direction of your eye strike your retina, and your brain goes "Hey! That thing is red!".

And that's how we get things with color. If its a light bulb, it's a particular color because that's the color (frequency) that it's electrons give off vibrations at. If it is just a plain old object, it's a particular color because its electrons don't vibrate at that color.

Isn't physics fun? Or should I say, phun?

Homemade Mallowmars

Mallowmars, if you have never heard or tasted one, is a chocolate dipped, marshmallow-topped cookie that is about the size of a girl scout cookie, and can only be found in colder weather in many of the United States. Incidentally, there are a million variations on this cookie and no one knows who invented it.

Growing up in New Jersey, we couldn't always find them, so they were (and are) are a real treat. So when I wanted to make something nice for my mother, I thought I would make homemade mallowmars, because if I'm going to do something, I may as well do it in the most labor intensive way possible, yes? Or it's because it allows me to make cookies, candy and chocolate dip something all for one purpose.

Making these things is time consuming, but not 'difficult' in the way that making a baked alaska is difficult. It takes a lot of steps, but no one step is tricky.

Step 1: make the cookie base. I used a half batch of the "Joy of Cooking" sugar cookie dough, using an 1.5 inch cookie cutter, and it yielded a 100 bases.

You want to have extras, for testing at every step and to allow for failure (cookie cracks, flips over in the marshmallow stage, chocolate coating doesn't cover evenly). I had about a 10% loss  from start to finish, but your results may vary depending on the number of people who insist on taste testing and your ability to handle things with fingers covered in culinary superglue.

Step 2: Pipe on marshmallow. This requires some hand strength, or ingenuity. Preferably both. This is the biggest 'cookie down!' part, because if the cookie lands marshmallow side down, (as you can see happened to two in this picture) there's no hope for that one. I use Alton Brown's recipe, which has never failed me. Actually, I don't think I've ever had a recipe of his fail.

Step 3: After letting the marshmallow set for  4 hours, melt some chocolate. I like Ghiradelli 60% cacao chocolate chips, because they melt the best to give a not too thick, even coating and keep the temper the best. I melt them in a double boiler, because it yields the smoothest result.

Step 4: Dip the cookies in the chocolate, let sit overnight to set. Enjoy!

They may not be as pretty as the ones that come out of a box, but they taste a whole lot better. And totally worth the effort.