How Do Object Distance and Focal Length Affect Depth of Field?

Note: this is Part 2 of a series on depth of field. Click here for part 1, which explains the relationship between aperture size and depth of field.)

Besides using aperture size, photographers can also control depth of field by changing the camera-to-object distance or the lens focal length. Specifically:

  • For a fixed focal length and aperture size, increasing the object distance will increase the depth of field.
  • For a fixed object distance and aperture size, increasing the focal length will decrease the depth of field.

These two effects are closely related, and the quest to understand them offers a great example of how we can use equations to augment our intuition while solving relatively complicated problems. Read on if you want to learn more!

Click here to continue


The Secret Lives of Electrons

It’s not much of an exaggeration to say that electrons form the backbone of the modern world. They are our workhorses—they bring energy from power plants to our homes and factories. They are our couriers—they carry information through circuits in our computers. Some day, they will be our providers—as the central elements in photovoltaic solar cells, they will capture the sun’s energy for our use. These current and future electronic devices rely on very precise answers to the question What do electrons do inside materials? Out of technological need and intellectual curiosity, condensed matter physicists have spent over a century discovering better and better answers—and they continue to do so today. In this post, I will try to give you a little glimpse into the form, beauty, and utility of such an answer.

Current And Future Electron Usage -- Energy Transport, Information Encoding, Energy Generation

Click here to learn more about electrons!

Snowy Ithaca Falls

To celebrate the summer solstice, I thought I’d share some interesting sights I saw at Ithaca Falls after a snowstorm.

Parts of the waterfall froze but the rest kept moving. I thought it would be cool to take a long-exposure shot to contrast the slow and fast H2O.

Ithaca Falls - Slow Shutter

Of course, I wasn’t the only one taking pictures—the falls draw a nearly constant stream of visitors on cold days. The cute girl in the pink hat is my girlfriend Heidi; the two guys are random strangers. This is my favorite picture from this shoot; the wall of water and ice looks almost too fantastic to be real.

Ithaca Falls - People

Most of Fall Creek was covered with ice, but the rushing water at the base kept a small area clear. Heidi thought it looked deceptively like a hot spring.

Ithaca Falls - Hole in Ice

The constant wind blowing from the waterfall creates some unusual ice structures. For example, these crystals were growing horizontally on the gorge walls near the falls:

Ithaca Falls - Cool Ice

When I looked up to the top of the gorge, the dusting of snow on the jagged walls made them seem to be drawn in white:

Ithaca Falls - Upwards

The Machine Shop

Using the machine shop is one of the best things about working in an experimental physics group. I love the machine shop! Words probably cannot describe its awesomeness, but I’ll try anyway: grinding tool bits is like meditating. Using the lathe to peel away an oxidized surface—thereby revealing the shining fresh metal underneath—is like magic. Everything is sharp, weighs alot, and/or moves fast. And successfully finishing a complicated part brings supreme satisfaction.

Speaking of that—I just finished a complicated part! It’s a phosphor bronze flip stage for a new ARPES sample manipulator. (I realize that doesn’t mean anything to most people, but I’m including its name for completeness.) It took me a few weeks to complete. (And I couldn’t have done it without a lot of help from Nate, Supreme Machinist and Overlord of the Graduate Research Shop.) I’m really excited and want everyone to see it! So here it is:

Flip Stage 1

Flip Stage 2

Flip Stage 3

The colorful areas are regions of oxidized bronze. I didn’t thoroughly clean the oil off my part at one point, and after sitting around for a few days, the surface started to oxidize. The lines on the bottom are marks from the CNC that I used to mill out the protruding rectangles. The circular scratches around the central hole are from a Brillo pad.

Here are a few shots from the machining process. The first shows the CNC in action, milling away the bottom of my part. There’s a long bronze chip stuck to the cutter, spinning around.

CNC Action Shot

Here’s a cleaner version so you can see what the CNC did. Isn’t it pretty?

Somewhat Symmetric

This shows my method for holding the part when it got too thin: I had to bolt it to an aluminum block. In this picture, I have used a thirty-degree parallel to hold the part on an angle.

Angled Part

Finally, if you’re interested, here’s the entire process of what I did to make the part:

The Flip Stage Process

  1. I got a stock bronze cylinder.
  2. It was too big, so I had to cut down its length. First I used a band saw, then I faced off the uneven cuts with a lathe to make sure the ends of the cylinder were parallel.
  3. I then made it into a box. I made rough cuts with a band saw, then used a mill to ensure all the faces were parallel/perpendicular to each other.
  4. A drilled a few holes on one end using the mill.
  5. I held the part in a four-jaw chuck on a lathe and lined up the largest hole with the lathe’s rotation axis. Then I turned down the box into a cylinder.
  6. I flipped it upside down and made a few more holes with a CNC.
  7. I used the CNC to remove material around a few rectangles on the bottom.
  8. It might be hard to see in this picture, but I used the CNC to make a small counterbore at the end of the protruding cylinder.
  9. I cut away a large piece of the box to leave an “L” shape.
  10. I milled away part of one end.
  11. It might be hard to see in this picture, but I angled the sides. This necessitated turning the whole mill head by fifty degrees.
  12. I made another small counterbore on the other side of the protruding cylinder.

The Christmas Beef

This literally has nothing to do with physics, science, or good taste—but it’s funny. It’s a short story that I wrote on a whim during my freshman year of college. I think it’s destined to become a Christmastime classic. Someday, you’ll be watching animated versions of The Christmas Beef on TV with your kids all through December. So, without any further ado, here it is:

The Christmas Beef

Once upon a time, there was a family called the Salisburys. It was a small family; just Mama and Papa Salisbury and their young son, Peter. They lived together in a tiny single-room shack. It was the dirtiest shack in the dirtiest corner of the dirtiest city on the planet. Dirt was piled on the floor, and it sat inside the cupboards, and it flowed out of the faucets. Dirt was really the only thing that the Salisburys had a lot of. If dirt was currency, they would have been richer than kings—but it wasn’t, so they were just poor. To speak bluntly, life was not quite as good as it really could have been for the Salisburys. Things had once been better, but that was ages ago.

Papa Salisbury’s great-grandfather, Philiminster Salisbury, was the inventor of the Salisbury steak. Through a clever marketing scheme, Philiminster became a millionaire, and the Salisbury family lived in luxury. However, Philiminster’s son, Gerald, invested all of his father’s money in some very high-risk stock from a dirt factory. He lost the fortune, but in an ironic twist of fate, his family acquired a very large and seemingly inexhaustible dirt supply. Ever since then, the Salisburys had been caught in a never-ending downward spiral. Each successive generation was worse off than the one before it. By the time that poor little Peter was born, the Salisburys had not only lost their money, but also their good looks and intelligence.

Our story starts in the wintery months of little Peter’s ninth year. Christmas was just around the corner. It was a magical time for everyone. People were bustling about on the streets, buying presents for loved ones. Salvation Army Santa Clauses were filling the air with the sound of bells. Christmas lights were hung everywhere. Snowflakes fell from the sky and hot chocolate was always waiting inside. Well, it was magical for everyone except the Salisburys. They couldn’t exactly afford to buy anything, because dirt still wasn’t worth any money, and the sight of so many other happy people just served to highlight their own unhappy lives. So, all through the Christmas season, the Salisburys just sat inside and moped.

Little Peter’s favorite winter pastime was to make dirt angels. The Salisburys couldn’t afford toys, of course, but they had lots of dirt. So little Peter would go to the dirtiest corner of the shack, pile up the dirt, and lay in it. Then, by waving his arms and legs around, he would make the shape of an angel in the dirt. One day, God happened to look down at Peter’s shack and see one of those little dirt angels. He was so moved by pity that he sent down a real Dirt Angel to look after Peter. Peter couldn’t see his Dirt Angel, of course, but he was always there, watching over little Peter. His name was Horace.

On December 24, as Peter was making a dirt angel in the corner, his mother began to cry. She had been working on making dinner, which was going to be dirtburgers and dirt soup, when suddenly she burst into tears. “What’s the matter?” asked Papa Salisbury. “It’s just that I feel so bad for Peter,” she replied. “He won’t be getting any presents this year, and on top of that, we can’t even afford a decent meal. I wish so badly that we could have some beef so I could make him a real dinner. I wish he didn’t have to eat Prime Dirt tomorrow night while everyone else in the world was eating Prime Rib. If we could just have some beef in the house for him, it would make me happier than anything else in the world.” Peter got up from his dirt pile and hugged his mother.

Later that night, after dinner, when Mama and Papa were asleep in their beds, Peter quietly drew back his dirt comforter and walked outside. He sat down in front of the little shack and thought. He thought long and hard. He wanted his parents to be happy. He wanted to be happy. He was sick of his horrible life and all the misery around him. Finally, in an act of desperation, he yelled out into the cold air, “I wish I was beef! Then Mama would be happy!” At that very instant, Horace stepped out from behind a nearby dumpster. “Who are you?” cried Peter. “I’m Horace,” answered Horace. “I’m a Dirt Angel. I’ve been sent here to watch over you, and I think I can help you out.” The angel took a step forward, genuflected, and knelt down. Then he muttered a low unintelligible prayer. A light shone down from the sky onto Peter, and he suddenly turned into beef. Horace smiled and sped away toward heaven.

When morning came around, Mama and Papa Salisbury climbed out of their dirt bed and looked around. “Where’s Peter?” they both exclaimed at the same time. They quickly searched all twenty square feet of the shack, but he was nowhere to be found. “Maybe he went outside,” thought Mama Salisbury. She opened the door. There, sitting on the ground in front of her, was a nice hunk of raw meat. She brought it inside, confused. “Oh well,” she thought, “I’ll deal with that later.” Mama and Papa searched the neighborhood for hours, but eventually reluctantly admitted that Peter was gone for good.

The day passed in sullen silence until it was time for dinner. After Mama prepared it, she and Papa sat down and said their prayers. “It really is a shame,” said Papa a minute later, in between mouthfuls of succulent beef, “that Peter couldn’t have been here to enjoy this delicious Christmas meal.”

Slea Head Drive

(Part three of a series of posts about my vacation to Ireland. Part one was Skellig Michael and part two was Newgrange.)

Beauty—natural or otherwise—was certainly the common theme to most of Heidi’s and my activities in Ireland. Our thirty mile bike trip around the Dingle Penninsula—known as the “Slea Head Drive”—was no exception. It was quite a big bike ride, so I’ll have to make quite a big post to talk about it.

The General Scenery

It was overcast and misty for most of our bike ride. Although this is apparently typical for Irish weather, it was one of the only non-sunny days of our vacation.

The Start of the Slea Head Drive

We biked around the peninsula in a big clockwise loop. The interior was on our right side and mostly consisted of fields and hills. Much of the land was occupied by farms and their associated livestock:

Sheep and Cows

The ocean was on our left. Land met water in steep cliffs:


And off in the distance, we could see stunning seascapes:

Dingle Seascape

The Fort

The Slea Head Drive passes by quite a few interesting landmarks, and I’ll put some of my favorites up here. The first is Dún Beag Fort. It was built around 500 BCE and sits right at the edge of a cliff. It has two stone walls and a few earthen walls (read: mounds of dirt) that surround a sheltered interior. (It is protected from the rear by the cliff.) There are several cavities in the walls, and there is even an underground passageway called a “souterrain.” (You can go in the cavities/rooms but not in the souterrain.) The fort’s original purpose is unknown, but its small size and simplicity seem to preclude it being a permanent settlement. It was probably used to protect cattle from raiders.

Dún Beag Fort

Natural erosion has caused some of the fort to fall into the ocean, but other than this, it is very well preserved. This is pretty typical for prehistoric Irish structures. Ireland’s first inhabitants built many elaborate stone buildings and monuments, but they later left their lands. Newcomers arrived, and lacking any other explanation, assumed these structures were built by Faeries. Superstitious fear prevented these people from entering or defacing any ancient sites.

The Beach

A few miles away from the fort, I was somewhat surprised to find a pristine beach with blue-green water and warm yellow sand. There’s not much to say about it, but it sure was beautiful:

The Beach

The Brewery

Near the end of the trip, Heidi and I passed a microbrewery called Beoir Chorca Dhuibhne. I thought it might be a mirage at first, but it was real! After visiting an endless series of bars that only served Guinness and Smithwick’s, we had despaired about ever finding any unique Irish beer. This brewery restored our faith in Irish alcohol; their beer was delicious! I liked it so much that I bought four bottles (all that would fit in my bag) and carried them on my back for the remaining six or seven miles of our bike ride. I eventually brought them back to America as presents for my parents, who also loved them. If you’re ever in Dingle… please visit Beoir Chorca Dhuibhne! As an added bonus, the bar is located in a three-hundred-year-old farmhouse.

Dingle Brewpub

The Church

After having a beer at the brewery, we hit the last landmark of our trip: the Gallarus oratory. It’s a mysterious old stone church—both its age and the meaning of its name are not known with any great precision, although it was probably built between the sixth and twelfth centuries AD.

It’s a cool-looking building, but there is really only one good angle to take a picture of it. So:

This is my picture of Gallarus Oratory. There are many like it, but this one is mine.

Gallarus Observatory

According to a pamphlet I picked up at the Oratory,

The oratory was built by early Christians who loved their trade. Life was much simpler then, and men understood God and His ways much better than they do now. Successive invaders—Vikings and Normans—burned, robbed, and destroyed the settlements around Gallarus and a beautiful way of life was lost forever.

I like that description for some reason.

The Dinner

We finally got back to Dingle (after making a few wrong turns) just in time to return our bikes to the rental store and set up a reservation at the best restaurant in town—Out of the Blue. It’s a seafood restaurant that serves only fresh fish from the previous day’s catch. If there’s no good fish, they don’t open—it’s as simple as that. I got an awesome sea bass:

Sea Bass from Out of the Blue

Which I promptly devoured:

Kick His Ass, Sea Bass!

The Best Part

I temporarily abandoned chronological order so I could save my favorite part of the trip for the end. It was a detour I took to walk down an unmarked gravel path.


After I passed the first hill, the landscape started getting a little strange. Sparse stones randomly jutted up, and the ground was covered by low stiff bushes.


Looking back, I could still see the warm beach and much of the peninsula:

Looking Back

But in front me there was an increasingly rocky passageway:

Rocky Passageway

After I passed through the rocks, the path ended with a sheer cliff, and I found myself at the end of a long strip of land that stuck out into the Atlantic ocean. I was all alone. It was an amazing feeling. I had spent all day biking around—which tends to decrease the intensity of my thoughts, and to increase the sensation of being in the moment. Now I was sitting directly in the midst of the cliffs, hills, and water I had earlier seen from a distance. I felt like Wang Wei in his poem Deer Enclosure:


Empty mountain: no man.
But voices of men are heard.
Sun’s reflections reaches into the woods
And shines upon the green moss.

I felt like I had melted into my surroundings. Eventually I heard people behind me and the spell was broken. I turned to my side and took a picture of another far-off chunk of land jutting into the sea. I imagine mine must have looked similar from over there…

Looking to the Right

The Conclusion

Overall, Dingle was pretty awesome. Where else can you get stuck in cow traffic while biking? (Seriously!)

Further Reading

Non-visual Vistas, Non-spatial Travels

As some of you know, I am currently a graduate student in an experimental condensed matter physics research group. I’m sure that physics graduate school is quite mysterious to people who aren’t in it, and one of my goals for this blog is to explain what I do there and why I choose to do it. I hope my thoughts can be useful to both prospective physics students and to my non-physicist friends and family.

This certainly is a big task, and there’s no chance of me completing it in a single post. Instead, I’d like to start by telling you about the “a-ha moment” when I suddenly realized that condensed matter physics was interesting. It happened on Friday, March 6, 2009, sometime between 3:20 PM and 4:40 PM. It was the spring semester of my sophomore year of college; I was sitting in my thermal physics class, and we were learning about phase diagrams. In particular, my professor showed us the phase diagram for H2O, which I will now show you:

Water Phase Diagram

There is a clear scientific meaning to this picture. Each point on the diagram represents a pressure value and a temperature value; the diagram itself tells us whether H2O will be a solid (ice), liquid (water), or gas (steam) at that particular combination of temperature and pressure. The thick black lines show the locations of phase transitions where H2O changes from one phase to another.

Until this point in my life, I had always felt a sort of impersonal interest in physics. But something suddenly “clicked” when I saw this phase diagram. I had a big realization—that scientific facts really only come alive when interpreted by a human and related back to human experience. I don’t know why this happened. It may have been that I had finally matured enough to realize this, or I may have just needed something special to come along and shake me out of my “scientific stupor.” At any rate, I had an epiphany, which I would now like to share with you.

The first thing to notice is that the phase diagram contains all of our common experiences with H2O. Atmospheric pressure at the surface of the Earth is around 1 bar, which you can find as a horizontal line on the graph. As we travel along this line from low temperature to high temperature, we see that H2O changes from ice to water at 273 K (equivalent to 0°C or 32°F) and from water to steam at 373 K (equivalent to 100°C or 212°F).

Water Phase Transitions at Atmospheric Pressure

The second thing to notice is that the phase diagram contains so much more than all of our common experiences with H2O! People live at pressures near 1 bar and only deal with temperatures between 0-100°C, but H2O exists in a much wider range, and it does many other things besides melt and boil. Let’s discuss three of them:

  1. At low pressures—say, 0.001 bar—water does not exist at any temperature. H2O goes straight from ice to water vapor in a process called sublimation.
  2. There is a single point on the diagram where ice, water, and steam can all coexist. (I marked it with a red dot.) It is located at a pressure of 0.006 bar and a temperature of 0.01°C. Imagine visiting a planet whose atmospheric pressure was 0.006 bar. Water would only exist if the temperature was exactly 0.01°C. If you tried to melt ice, you would find that it simultaneously turned into both water and steam! (The picture below shows solid argon doing this at atmospheric pressure.)
  3. There is another special point where the dividing line between liquid and gas simply disappears. (I marked it with a blue dot.) It is located at a pressure of 221 bar and a temperature of 374°C. At greater temperatures and pressures, there just isn’t a difference between liquid and gas. An interesting consequence of this is that you could turn water into steam without boiling it if you could first raise its pressure to 230 bar, then increase its temperature to 380°C, and finally decrease its pressure back down to 1 bar.

Argon Ice Simultaneously Melting and Sublimating

In one sense, H2O’s phase diagram vividly demonstrates how narrow the human experience is. (Well, it demonstrates one aspect of a much larger narrowness.) We think that ice melts into water, but sometimes it sublimates into steam, and sometimes it does both. We think of water and steam as totally different, but under some circumstances, they aren’t. Living at a single pressure is like always looking in the same direction. Learning about this phase diagram is like suddenly turning your head to the left and right. A whole new vista becomes visible.

In another sense, the diagram shows that even boring everyday substances can become interesting when they’re subjected to unusual conditions. People like to travel because new and different surroundings are fun and exciting; physics teaches us that changing spatial coordinates is not the only way to achieve this effect. Moving to exotic temperatures and pressures is a whole new way to travel.

We can ask a lot of questions about phase diagrams. For example:

  • Do all substances have similar phase diagrams?
  • If not, what changes between substances? Are there certain groups that have similar phase diagrams?
  • Why are different phases stable in different regions?
  • Can we predict the phase diagram for a particular substance?
  • Are there other kinds of phases besides solid, liquid, and gas?
  • Are there other parameters besides temperature and pressure that can change a substance’s phase?
  • Are there different kinds of phase transitions?

Answers to these questions can satisfy out natural curiosity about the physical world and lead to new technological applications. One goal of condensed matter physics is to answer them as fully as possible.

Phase diagrams didn’t point me unambiguously towards condensed matter physics, but they did open my mind to it. They taught me a new way of thinking, and they opened my internal eyes to viewless vistas. Ever since that day in March 2009, I have had a soft spot for them in my “physics heart,” and I hope you can at least partially appreciate why.


  • The data for the melting and sublimation lines of water are from “International Equations for the Pressure along the Melting and along the Sublimation Curve for Ordinary Water Substance”, J. Phys. Chem. Ref. Data, Vol 23, No 3, 1994.
  • The data for the boiling line of water are from IAPWS formulation for Industrial Use, 1997.
  • The picture of argon ice is from