Physics on Victor42

Why Isnt the Summer Solstice the Hottest Day of the Year

hi@victor42.work (Victor42) — Wed, 23 Jul 2025 16:54:00 +0000

For most of China, the dog days of summer are just around the corner. July and August bring a special kind of misery where a quick lunch run can feel like you’re losing a layer of skin. Late last August, a colleague and I pondered why summer drags on for so long. His theory involved some myth I can’t recall, but I confidently declared, “It’s the concrete. It soaks up a ton of heat and takes a couple of months to let it all go.”

I immediately knew that sounded a bit too simple. It felt right, but it wasn’t very scientific. So, today, let’s get to the bottom of it.

We all know the summer solstice hits around June 21st. It’s the longest day of the year in the Northern Hemisphere, when the sun is directly over the Tropic of Cancer (23.5°N latitude, near Shantou).

In theory, this is when we get the most solar radiation. After the solstice, the sun’s direct rays head south, and the days start getting shorter. So why are July and August even hotter?

It Starts with a Lag

Let’s begin with something we see in daily life.

Think about this: if you live in a concrete building, you’ve felt how it stays cool in June even when it’s hot outside. Opening a window is pure bliss. But come September, the crisp autumn air is a lie the moment you step inside your oven-like home.

This is especially true in South China during the “Huinantian” (Resurgence Days) in May and June. Hot, humid air condenses on the cool indoor surfaces, turning walls and floors into a dewy mess. This proves that buildings have a significant thermal lag.

My concrete theory was looking good until I remembered the 24 Solar Terms. Our ancestors knew about the “dog days” of summer long before concrete existed. This phenomenon is older than our cities; it’s baked into the Earth itself.

Earth, the Giant Thermos

To understand this, picture the Earth as a giant thermos, its surface a mix of oceans and land.

The ocean is a massive water tank with an incredible ability to store heat. It can absorb huge amounts of energy with only a slight temperature increase.

Land is more complicated. It’s a mix of water, rock, soil, and man-made structures.

Water is the key player, acting like a sponge for heat. It’s a small part of the land’s mass but holds the most heat.

Rocks and soil, on the other hand, are terrible at long-term heat storage. They have a lower specific heat capacity and are poor conductors. I once visited the Mingsha Sand Dunes in Dunhuang, where the surface sand was scorching, but just a few inches down, it was cool. The heat doesn’t travel deep.

Urban structures like concrete and asphalt are even more extreme. They have a similar heat capacity to soil but are darker, especially asphalt, which absorbs over 90% of sunlight. With no moisture, they can’t “sweat” to cool down. They bake all day and radiate heat all night, creating the urban heat island effect.

But none of this explains why temperatures keep rising after the solstice.

Here’s a better analogy: the leaky balloon. The sun pumps air into the balloon (Earth), while the Earth radiates heat back into space (the leak). On the solstice, the pumping is at its strongest. For two months after, the pumping weakens, but it’s still faster than the leak. The balloon keeps inflating.

Similarly, after the solstice, the Earth still absorbs more heat than it radiates. The planet’s heat reservoir keeps growing until, one day during the “dog days,” intake equals output. That’s the peak. After that, we finally start to cool down.

This is like “carbon peak.” It sounds bad, but it marks the point where the growth rate finally turns negative—a trend reversal.

In this process, water plays the decisive role. Water is the Earth’s most powerful “heat sponge,” capable of absorbing enormous amounts of heat with only a slight increase in its own temperature. The specific heat of water is 4-5 times that of sand and rock, meaning it can store far more heat in a much milder way.

The diurnal temperature range of a place is largely determined by the presence of water. In lush, vegetated areas with ample moisture, the temperature difference between day and night is small. In arid deserts, the difference is extreme.

To take it to an extreme, what if the Earth had no water or atmosphere? We have a perfect real-world example: the Moon. Without water as a “heat sponge” and an atmosphere as a “thermal blanket,” the heat absorbed during the day is almost entirely radiated away at night. The Moon’s surface temperature can soar to 127°C (260°F) during the day and plummet to -173°C (-280°F) at night. With such rapid heating and cooling, the phenomenon of thermal lag would cease to exist.

So, when we complain about the weather, let’s not forget the Moon. Our planet, thanks to the gentle “thermostatic suit” of water and atmosphere, has avoided becoming a hellscape of alternating extremes. They are one of the greatest miracles that allow life to thrive on Earth.

The Air Blower Barrel: The Subtropical High

But the Earth’s own heat accumulation isn’t enough to explain the suffocating heat of the dog days. The real knockout punch comes from an old acquaintance from the weather forecast: the subtropical high. What is it, exactly? A mass of air?

Yes and no.

Picture this: in a large river, a stable vortex forms in a specific spot due to the flow patterns. The vortex itself seems permanent, but the water molecules within it are constantly being replaced. The subtropical high is a magnificent, stable air vortex in the Earth’s atmosphere.

The one that affects China the most is the Western Pacific Subtropical High. Its raw material comes from the equator. Air, heated to a scorching temperature at the equator, rises to high altitudes and then splits into two streams, one north and one south. The northward stream cools at high altitude, sinks, and traces a huge arc, landing around 30°N latitude to form this massive high-pressure system.

If it’s a current of air, why doesn’t it just dissipate?

To understand its stability, we can imagine it as a bottomless, topless air blower barrel:

The Top: Hot air from the equator rises, deflects, cools, and sinks, continuously pouring into the barrel.
The Squeeze: The air pouring in compresses the space inside the barrel. This compression causes heating, resulting in a hot-over-cold air structure inside. This stratification prevents vertical convection. The hot air above acts like an invisible lid, letting air in but not out.
The Walls: The trapped air naturally tries to escape horizontally. But as it blows outward, it’s deflected to the right (due to the Coriolis effect in the Northern Hemisphere). At a certain point, it bends 90 degrees, creating a clockwise “wind wall.” Other air trying to escape from the inside collides with this wall, preventing the wall from deflecting further inward. These forces merge, strengthening the wind wall and creating a balance that contains most of the air.
The Leaks: At the bottom, however, this air barrel wall becomes less sturdy due to friction with the ground. It leaks air in various directions, forming the trade winds and westerlies.

We’ll discuss the “Coriolis effect” in detail in the next chapter; for now, just focus on the wind wall. Ever walk into a mall in the summer and feel that blast of air from an air curtain pointing straight down at the entrance? The door is open, but it’s two different worlds inside and out. That’s the blocking effect of a wind wall.

This is how this high-pressure vortex maintains its relative stability.

The subtropical high, this “air blower barrel,” is a living thing. Its shape and position are constantly changing. When it expands northward and envelops your city, the weather forecast will say the area is under its “control,” a very fitting term.

Imagine the scene from the movie Independence Day where the alien mothership slowly emerges from the clouds and hovers over the city—the subtropical high brings that same sense of oppression.

It makes you feel scorching hot in two main ways:

Sinking Air, Cloudless Skies: Inside the high, the air sinks. This presses the hot surface air down, preventing it from rising to meet the cold air above, which suppresses cloud formation. The result is a clear, sunny sky, allowing the sun to launch a direct physical attack on you.
Transporting Moisture, Muggy Heat: The high often packages and delivers the hot, humid air from over the tropical oceans. High humidity prevents your sweat from evaporating, effectively crippling your body’s cooling system. This is a magic attack.

It’s crucial to note the difference between how the body feels heat from ground radiation versus heat from water evaporation. The former is “sensible heat,” the latter is “latent heat.”

The ground radiates heat via infrared radiation, transferring some of its stored energy to your house, your body, and the surrounding air. The ground cools down, but for you, it’s a heating process—that roasting feeling you get on a summer evening.

When water evaporates, it absorbs a large amount of “sensible heat” and converts it into “latent heat” stored in the water vapor molecules. This heat, which was on the ground or on your body, suddenly seems to vanish into thin air. This is true cooling. Of course, the heat hasn’t disappeared; it’s just been carried away to the heavens by the water vapor.

So, in July and August, you can experience two very different kinds of summer heat. When you’re away from the subtropical high and only dealing with ground heat, it’s a relatively dry heat. You can ride a bike in the hot wind and barely break a sweat. When the subtropical high hits, it’s the kind of heat that makes your clothes stick to you, so muggy you don’t even want to speak.

These are two different summers. One is the summer of a vibrant, energetic high-school athlete; the other is the summer of a sweaty, stressed-out recent grad hunting for a job.

The Coriolis Effect

Now let’s dive into the Coriolis effect, also known as the geostrophic deflection force, and see where the “barrel wall” comes from.

This force is fascinating. It’s not a real push or pull but an inertial phenomenon.

Imagine a cannonball fired from the equator, aimed straight for the North Pole. There are two ways to understand the Coriolis effect.

From the perspective of an observer on the ground:

When the cannonball launches from the equator, in addition to its northward velocity, it carries a huge west-to-east inertial velocity from the Earth’s rotation (about 1670 km/h or 1040 mph). As it travels north, the latitude increases, the circumference of the latitude line decreases, and the rotational speed of the ground below it slows down. But the cannonball, due to inertia, maintains its high equatorial speed. Consequently, it “outruns” the ground beneath it, causing its path to curve eastward. For a northbound cannonball, this is a deflection to the right.

Conversely, if fired from the North Pole towards the equator, the cannonball’s initial east-west velocity is zero. As it flies towards the equator, the ground beneath it is moving eastward at an increasing speed. The cannonball “can’t keep up” and lags behind, deflecting westward. For a southbound cannonball, this is also a deflection to the right.

From a God’s-eye view:

Watching from space, you’d see the rotating Earth move the cannonball to the side. You’d notice that when the cannonball launches from the equator, its initial direction isn’t straight up but diagonally up and towards you. Ignoring gravity, it would travel in a straight line in space. But gravity pulls on it, essentially “taping” this straight line onto the Earth’s surface, making it follow a “straight line on a curved surface.” This is also known as a great-circle route, the shortest path on a sphere. You can see this by stretching a string on a globe. The cannonball would travel northeast, reaching a high latitude where its direction is due east, then curve southeast, its latitude decreasing until it returns to the equator.

It was aimed north, but it passes the North Pole to the northeast. To someone on the ground, doesn’t that look like a rightward deflection?

So, the Coriolis effect isn’t a force; it’s an illusion. We are spinning but often forget we are. We only realize something is amiss when things don’t travel in the straight lines we expect.

The famous Foucault pendulum experiment in science history used this principle to prove the Earth’s rotation. It’s also why atmospheric phenomena are always spinning.

But wait! Sharp-eyed friends might spot another issue. What if the cannonball is fired horizontally at a mid-latitude, with no initial north-south velocity? Why does it still deflect? The “different speeds at different latitudes” explanation doesn’t seem to cover this.

Congratulations, you’ve entered the deep end of the Coriolis effect. You’ve discovered an important fact: physically, the Coriolis effect isn’t driven by a single principle. The north-south deflection is mainly due to the conservation of angular momentum, but the east-west deflection is primarily caused by the balance of centripetal force.

First, let’s reiterate an important concept: Gravitational Force ≠ Gravity.

Gravitational force (F) is due to the Earth’s mass; it exists whether the Earth spins or not and points towards the Earth’s center. Centripetal force (f) only exists with rotation; the faster the spin, the more centripetal force is needed. It points perpendicularly towards the Earth’s axis of rotation. These two forces have different directions. The part of the gravitational force that remains after accounting for the centripetal force is the gravity (mg) you feel. Of course, since gravitational force is very large and the required centripetal force is very small in comparison, the direction and magnitude of gravity are very close to that of the gravitational force.

Note that gravitational force is constant, while centripetal force isn’t a force an object actually receives; it describes the force required for an object to maintain its orbit at a certain speed.

So, for a cannonball at rest, the gravitational force is constant. The component of gravity in the direction of the centripetal force (let’s call it the centripetal component) provides just enough force to keep it stationary.

If fired eastward, the gravitational force is unchanged, but its orbital speed is now its own speed plus the Earth’s rotational speed. It’s moving faster than its latitude. The centripetal component of gravity can’t provide enough force to hold it. It has a tendency to fly off into space, opposite to the direction of the centripetal force. This outward tendency can be split into two components: one perpendicular to the surface and one along it. The perpendicular one doesn’t affect deflection but creates the interesting Eötvös effect (which we won’t get into, or we’ll never finish). We’re interested in the motion along the surface. The cannonball will move towards a lower latitude where more centripetal force can be provided. So, it moves south, deflecting to the right.

If fired westward, the same logic applies. Its combined speed is slower than its latitude. The centripetal component is now excessive, creating a tendency to pull it towards the axis of rotation. Along the surface, this manifests as a northward movement, which is also a rightward deflection.

Once it deviates from a pure east-west path, the angular momentum factor starts to play a role in the north-south direction, ensuring the cannonball continues to deflect.

Studying this leaves a strange feeling. How can this be? Can multiple physical laws combine to form a new one? Is this some kind of nesting doll? But mathematicians see it differently. The formula they derived for the Coriolis force is:

$$ {\displaystyle {\vec {F_{c}}}=-2m({\vec {\omega }}\times {\vec {v}})} $$

I won’t explain it in detail, but this formula covers both east-west and north-south cases simultaneously. Oh, so two different things in physics are the same thing in math… Sorry, my mistake.

Let’s stop here with the Coriolis effect. We have enough information to explain the thermal lag. In short, the existence of the Coriolis effect allows the subtropical high to maintain its “barrel wall,” trapping the high-pressure air inside and creating this unique atmospheric phenomenon.

A quick reminder: in everyday life, the Coriolis effect is not very noticeable. The direction of the vortex in your toilet or sink drain is mainly determined by the shape of the basin and the initial disturbance of the water, not this force.

The Conspiracy of the Thermos and the Air Blower

Alright, back to the main topic. We can now summarize. After the summer solstice, two factors conspire to keep the weather getting hotter:

The Thermos: The Earth’s continued accumulation of heat.
The Air Blower: The external heat delivered by the subtropical high.

Which factor has a greater impact? That’s like asking in a gas explosion whether the gas or the spark is more to blame.

The heat stored by the land, especially by the “heat sponge” of water, is the gas filling the air. It determines the baseline and duration of the heat. On one hand, it stores a massive amount of heat in early summer, preventing the surface temperature from rising too quickly, which is why the solstice isn’t the hottest day. On the other hand, the heat it has accumulated peaks in July and August, finally causing a significant rise in near-surface temperatures, creating a kind of “stone pot bibimbap” baking heat.

At this point, the intense heat is like gas filling the air, just waiting for a spark.

And the humid, scorching blast from the subtropical high is that fatal spark, making you feel like you’re about to explode. This is the inescapable reality of the dog days of summer.

Well, after all that, I know you don’t feel any cooler. Neither do I. Even the toothpaste in my bathroom is warm.

Finally, on the topic of summer, you might also be interested in this: Why Can the Summer Sun Shine on a North-Facing Wall?

How Does Water Put Out Fire

hi@victor42.work (Victor42) — Wed, 25 Jun 2025 20:50:00 +0000

This question just popped into my head. I bet my daughter will ask it when she’s a bit older. Pause for a moment and think, how would you answer it?

Think carefully. A serious answer, please. No wise cracks.

This detailed explanation is probably best saved for when my daughter is in middle school. If she asked me right now, I’d probably just say, “Because water cools things down, so the fire can’t keep burning.”

But that’s fine. I’m the one who’s curious, so let’s dive deeper.

What is Fire?

To understand how to extinguish a fire, you first have to understand fire itself.

High school chemistry taught us that combustion requires three elements, forming the “fire triangle”:

Fuel: Something that can burn, like wood or gasoline. These are essentially reducing agents.
Oxidizer: Something that helps things burn, usually oxygen from the air. These are oxidizing agents.
Heat: Something that provides the initial energy, like the heat from a match.

All three must be present.

By the way, oxygen isn’t the only oxidizer. Hydrogen can burn in chlorine, and many substances burn violently in fluorine. It’s just that on Earth, oxygen is the most common one.

This is a scientific approach: for water to put out a fire, it must remove at least one of these three elements. Which one? Let’s hold that thought and dig deeper.

Now, let’s step into the microscopic world of chemistry and see how these three elements ignite.

Here’s a little-known fact: liquids don’t actually burn. The vast majority of combustion we see happens in the gas phase.

At a microscopic level, combustion is a rapid, violent oxidation-reduction reaction where fuel molecules and oxidizer molecules collide at high speed, turning into other molecules and releasing light and heat. For efficient collisions, the best state is a gas, where everything is thoroughly mixed.

Let’s do a thought experiment with a cup of gasoline. We’ll put it in a special device that’s both a freezer and an oven, and slowly heat it from near absolute zero (the coldest temperature in the universe) without an open flame:

At about -40°C, gasoline molecules gain enough energy to evaporate from the liquid surface into a gas. This gasoline vapor spreads into the air, with higher concentrations near the liquid surface. A quick spark will ignite this thin layer of vapor in a “poof,” and then the flame will extinguish. This temperature, -40°C, is the flash point of gasoline; from this temperature on, it can be ignited.
Continue heating. At about 280°C, something amazing happens: even without an external heat source or a spark, the gasoline suddenly bursts into flame and burns until it’s gone. This is the autoignition temperature. At this temperature, the collisions between gasoline vapor and oxygen molecules are so violent that for every molecule that burns, the heat it releases vaporizes another one from the cup.

See? The secret to a sustained flame is the evaporation rate. The hotter it gets, the faster it evaporates. At the autoignition temperature, the rate of vapor production meets or exceeds the rate of consumption by burning. Once this fuel supply line is established, combustion becomes a self-sustaining positive feedback loop.

The Peculiarity of Solid Combustion

The combustion of solids is more complex than that of liquids. Let’s use burning wood for another thought experiment.

The burning of wood occurs in two stages:

Stage 1: Flaming Combustion.

When wood is ignited, the complex organic macromolecules inside it break down in a process called pyrolysis. Pyrolysis produces two things: flammable gases (like methane and carbon monoxide) and solid charcoal (which is almost pure carbon).

This process is similar to liquid combustion, but “evaporation” is replaced by “pyrolysis.” Evaporation is a physical change—the molecules themselves don’t change. Pyrolysis is a chemical change—large molecules break down into smaller gas molecules. These flammable gases mix with the air and burn, creating a beautiful flame around the wood. Since hot gas rises, flames always appear at the top.

Stage 2: Smoldering.

When most of the gas has burned off, the flames disappear, leaving glowing red embers. Flaming combustion is over, and the flameless smoldering phase begins.

This process is more like a close-quarters battle. Oxygen molecules, the attackers, charge directly at the surface of the charcoal to react with the carbon atoms. The product, carbon dioxide, is a gas and flies away immediately. Fresh carbon atoms from below move up to the front line. This cycle repeats until the charcoal is consumed. The remaining ash consists of non-carbon impurities.

The pure surface combustion of charcoal has a huge advantage: it’s stable and controllable.

Its rate of heat release mainly depends on two variables: the fuel’s surface area and the oxidizer’s supply. The surface area is nearly constant, so the only variable is the oxygen supply. Therefore, its heat output can be precisely controlled, making it an ideal fuel, not just for its high heat value.

This property has special applications. Take steam locomotives, for instance, which burn coal (similar to charcoal). The fireman can control the fire’s intensity by adjusting the damper, which regulates the airflow into the firebox. This, in turn, controls steam production and the locomotive’s power.

Purple arrows show exhaust gas being expelled, which draws hot yellow-orange gas from the firebox. The firebox then sucks in fresh air, shown by the green arrows.

Even more clever is the blastpipe in the chimney. It ejects exhaust steam from the pistons at high speed, creating a vacuum that fiercely sucks fresh air into the firebox. This is based on the Bernoulli principle: the faster a fluid flows, the lower its pressure. The more the blastpipe blasts, the stronger the draft, the more oxygen enters the firebox, the hotter the fire burns, and the more steam is produced. It’s a brilliant positive feedback loop.

So, what if both the fuel and the oxidizer are solids? Does that kind of combustion exist?

Yes. The classic example is the thermite reaction. Mix aluminum powder (the fuel) with iron oxide powder (the oxidizer) and ignite it. The aluminum will snatch the oxygen atoms directly from the iron oxide. This solid-solid reaction releases temperatures up to 2500°C, hot enough to melt the resulting iron. The liquid iron allows the powders to flow, promoting continuous contact and sustaining the reaction.

To take it a step further, what happens if you strongly heat a solid fuel without an oxidizer?

It will only pyrolyze, not burn. This is a crucial part of modern chemical engineering. For example, heating coal without air (dry distillation) yields three important industrial materials: coke (for steelmaking), coal tar (a chemical feedstock), and coal gas (a fuel).

Now back to a fundamental question: Why does charcoal undergo pure surface combustion, while liquid fuels do not? This stems from differences at the molecular level.

Gas molecules are like rubber ducks in a pool, floating around randomly and bumping into each other.

Liquid molecules are like a pile of Buckyballs, held together by weak forces but able to slide past each other. This weak attraction is easily overcome by heat, allowing them to evaporate and escape.

Solid atoms (like carbon), however, are like a structure built with mortise and tenon joints. Each atom is locked in place by strong chemical bonds. The heat of combustion is not nearly enough to break this structure, so the atoms cannot escape as a gas and can only react on the surface. For instance, carbon’s autoignition temperature is a few hundred degrees, but its sublimation point (the temperature at which it turns to gas) is over 3600°C. It would have burned away long before it could vaporize.

The Essence of Combustion

By now, you might suspect the “fire triangle” model is a bit too simple. The conditions for brief combustion and sustained combustion are different.

Brief combustion: Requires fuel, an oxidizer, a temperature high enough for evaporation/pyrolysis, and an external ignition source.
Sustained combustion: Requires fuel, an oxidizer, and a temperature at the autoignition point.

The fire triangle model can’t explain why a flame is self-sustaining. So, scientists proposed the “fire tetrahedron,” adding a fourth element: an uninhibited chain reaction.

Once combustion starts, oxidizer and fuel molecules collide violently, creating new molecules and releasing heat. But that’s not the most powerful part of the chain reaction.

Besides collisions between whole molecules, many molecular “fragments” called free radicals are also involved. These are molecules that have been damaged in previous violent collisions. Some have lost an electron; others have an extra one. Free radicals are like hungry wolves, frantically attacking other molecules to become stable. This intensifies the collisions, generating more heat and more free radicals.

This process self-replicates and self-amplifies like a snowball rolling downhill. This is what makes fire so terrifying and magnificent. The power humans gained from mastering fire wasn’t just the heat of a torch against a wild beast. It was the leverage—a single spark could burn a prairie, providing cooked food and clearing land for farming. This power overwhelmed the physical strength of any other species.

Another chain reaction we’re familiar with is the one in an atomic bomb.

Speaking of which, what is an explosion? Is it brief or sustained combustion?

A (chemical) explosion is usually classified as brief combustion. When enough flammable gas has accumulated in the air at its flash point, a local ignition source reaching the autoignition temperature can trigger an extremely fast chain reaction. During the accumulation phase, the ambient temperature must remain below the autoignition temperature; otherwise, it would burn up before it could accumulate.

The Answer Revealed

Let’s summarize the microscopic combustion process:

Gaseous fuel: The most direct; burns when mixed with an oxidizer.
Liquid fuel: Must first evaporate into a gas.
Solid fuel: Mostly needs to first pyrolyze into a gas (flaming combustion), with the remainder undergoing surface combustion (smoldering).

As you can see, with few exceptions, most combustion follows the same path, shifting the battlefield to the gas phase.

Now, we can finally answer the original question. How exactly does water put out a fire? It attacks the “fire tetrahedron” on two fronts:

Attacking “Heat” (Cooling): This is water’s primary role. Water has an extremely high heat of vaporization; one gram of water turning into steam absorbs about 2260 joules of heat. To put that in perspective, that’s enough energy to lift a 100 kg (220 lb) person more than 2 meters (7 feet) off the ground. When water hits a fire, it absorbs a massive amount of heat, preventing the fuel from vaporizing and thus breaking the chain reaction.
Attacking the “Oxidizer” (Suffocation): This is a secondary factor. The huge volume of water vapor produced expands by more than a thousand times, displacing oxygen and stopping the combustion.

Of course, not all fires can be put out with water:

Electrical fires: Water conducts electricity and can cause electric shock or short circuits.
Oil fires: Oil is lighter than water and will float on top, spreading the fire as the water flows.
Reactive metal fires: Metals like potassium, sodium, and magnesium react with water to produce flammable hydrogen gas, essentially adding fuel to the fire.

Ultimately, the main reason water extinguishes fire is its powerful cooling ability. The same as the simple answer at the beginning.

But the journey of exploration is what’s interesting. An answer given without thought and one reached after a deep dive carry completely different weights.

If I’d known all this back in middle school, maybe I wouldn’t have failed chemistry.

Will Phones Ever Have 200mm Telephoto Lenses?

hi@victor42.work (Victor42) — Wed, 10 Jan 2024 17:57:00 +0000

I previously explored camera lens principles and “optical zoom” on phones: https://victor42.eth.limo/post-en/3645/

I noted that flagship phones typically have three cameras: a moderate focal length (20-35mm) for everyday shots, a shorter one (under 20mm) for ultra-wide-angle and macro shots, and a telephoto lens (over 50mm) for distant subjects.

So, will phones ever evolve to include 200mm or even longer lenses? Imagine photographing birds with just your phone! I’ve researched this further and have some new insights.

Longer Focal Length Means Longer Lens

First, I confirmed my hunch: longer focal length means a longer lens. The core optical component is the lens assembly, made of multiple convex and concave elements.

A fisheye lens, for instance, uses many elements to gather light from a 180° field of view, bending it gradually into nearly parallel beams. These are then adjusted to project a clear image onto the sensor.

Many factors influence lens length, and the internal optics are complex—far beyond my grasp. But focal length is key. To simplify, let’s recall basic optics: treat the assembly as a single lens.

Focal length is the distance from the lens’s center to the focal point. A lens with a given curvature always has a fixed focal point. The subject is usually much farther than twice the focal length (the third case above), creating a smaller, real image on the sensor.

The imaging formula is 1/f = 1/u + 1/v (f = focal length, u = object distance, v = image distance). With fixed f, the farther the object (larger u), the closer the image forms to the focal point (v approaches f). Since u is much greater than v, the sensor sits slightly beyond the focal point for a sharp image. Use a longer focal length, and the sensor must be farther away.

Thus, even a simple telephoto lens, with one element, needs that empty space to achieve its focal length. A complex, real-world lens also requires sufficient internal space.

This highlights the bottleneck: it’s physics. No matter how advanced technology gets, a 200mm lens can’t be as short as a 50mm one.

The Mountain of Physical Limits

Smartphones started sporting multiple rear cameras a few years back: a high-res main camera plus lower-res auxiliaries. These auxiliaries generally had focal lengths under 50mm. It’s not that manufacturers haven’t considered a “birding phone”—it’s physics.

Consumers do want telephoto lenses. Those who want them enough accept a price premium and a camera bump.

This is physics pushing back. Engineering yields. If a 50mm lens needs a bump, a 200mm one would likely be thicker than the phone. Phone birding seems impossible.

Smartphone history shows two trends in component performance:

Exponential growth: megapixels, storage.
Approximate logarithmic growth: focal length, screen size.

The first hasn’t hit limits; the second approaches them asymptotically. Portability limits focal length and screen size. They could grow, but the phone would become something else, exiting the mainstream.

Extending this, most physical limits (besides, say, light speed) are actually human body limits. Our bodies haven’t changed much in millennia, and civilization is built around them. Stair height, table height, traffic light colors, shower gel fragrance—all relate to the human body. Different humans would mean a different civilization.

Over the Hill

So, is phone birding truly impossible?

Let’s reframe: not “how to make a 200mm lens as short as a 50mm one,” but “how to fit a 200mm lens in?”

Shortening it is impossible, but fitting it in? That’s where ingenuity comes in. Limits can’t be broken, but they can be bypassed.

I recall seeing “periscope lens” on my phone’s spec sheet. I get it now. It bends light 90 degrees, like a periscope. The lens is too long for the phone’s thickness, so clever engineers used the phone’s width!

One of my phone’s cameras is square—a periscope lens hallmark. The square aperture and reflector boost light intake, compensating for the tucked-away lens.

Surging Forward

This reframes innovation for me. I knew the principle, but this made it click.

Clever innovations that solve big problems deserve praise. But these specific ideas aren’t as valuable as we think. Could only one person think of laying the lens down? The real challenge is committing resources to overcome the resulting hurdles.

Given time, these workarounds—bypassing limits with engineering—are inevitable. If one person misses it, another will likely propose something similar. Consumer demand, even latent, drives producers.

Semiconductor memory is cutting-edge, right? When processes approached quantum limits, some thought performance and capacity gains were over. But 3D stacking used vertical space, bypassing the limit and boosting capacity. The industry dances on the edge of limits, constantly breaking through.

What seems truly valuable is humanity’s collective innovative capacity—the flexible ability to explore, push boundaries, and maximize existing technology. A social structure that encourages, not suppresses, this is key to progress.

A Specific Heat Experiment in Your Dishwasher

hi@victor42.work (Victor42) — Thu, 09 Feb 2023 09:58:00 +0000

Specific heat capacity… Remember that term from physics class? What does it even mean?

If you own a dishwasher, you can easily demonstrate this concept to your kids (and yourself).

Here’s how: Place ceramic, glass (optional), stainless steel, and plastic bowls of similar size in the dishwasher. Run a normal cycle. Once finished, immediately open the door and watch the water droplets evaporate. Which bowls dry first, and which ones stay wet longest?

You’ll probably find that ceramic and glass bowls dry fastest. Metal and plastic ones may remain wet, especially in cooler weather. This is due to the specific heat capacity of each material.

Ceramic and glass have a higher specific heat than stainless steel. The textbook definition: the heat needed to raise or lower one unit mass of a substance by one unit temperature. Sounds complex? Simply put: for the same weight and temperature, ceramic and glass hold more heat than stainless steel.

Here’s a breakdown:

The dishwasher uses scalding hot water, heating all bowls until hot. While materials heat at different rates, given enough time and water, they’ll reach the same temperature.
Opening the door, the hot bowls use their stored heat to evaporate water. Only heat touching water aids evaporation; heat touching air dissipates.
Water droplets are evenly distributed. Assume the water-covered surface proportion is similar for each bowl.
Cooling to room temperature, the bowls release stored heat. Ceramic and glass release substantial heat, evaporating all surface water. Metal, storing less heat, remains wet even after releasing all its heat.

Two caveats. First: weight. Conveniently, similar-sized ceramic and glass bowls are usually heaviest. They’re thick to prevent easy breakage. Stainless steel, though denser, is strong and thin, thus lighter. This weight difference further increases the heat storage gap.

Second: heat dissipation. Metal conducts heat faster than ceramic. (That’s why metal pots are worse than clay pots for soup—another topic.) With rapid conduction, heat escapes easily where not blocked by water. So, despite similar water coverage, fast-conducting stainless steel loses more heat to the air. Little heat is used for drying. Before the water evaporates, the steel cools. This speed difference further increases the effective heat gap.

That explains the varied results.

Why so little on plastic? It’s a distraction. Plastic’s specific heat is higher than ceramic’s, but it’s far less dense. The significant weight difference makes other factors irrelevant. The minimal heat stored in plastic simply can’t dry the water.

Final tip: Season matters. If differences are subtle, try opening the door after 10, then 20 minutes. Trapped humidity slows evaporation, highlighting material differences.

Why Can the Summer Sun Shine on Your North-Facing Wall?

hi@victor42.work (Victor42) — Tue, 28 Jun 2022 14:18:00 +0000

As a kid, I was puzzled why sunlight hit the north side of my house in summer. Someone told me it was because the house wasn’t perfectly aligned. I believed this for years, even after learning enough in middle school to know better.

We often assume the sun rises due east, passes overhead at noon, and sets due west. Textbooks rarely challenge this.

Here’s a thought experiment using basic geography:

Near the equator (e.g., Singapore), on the equinoxes, a perfectly aligned house sees the sun rise due east and set due west. At noon, there’s almost no shadow.
Near the Tropic of Cancer (e.g., Shantou), on the summer solstice, the sun is overhead at noon. After noon, things get interesting. Visualize this: First, straighten the Earth to its equinox position. Rotate it from noon to evening; your house is on the day-night line. Finally, tilt the Earth back, facing the Tropic of Cancer towards the sun. At step two, a north-south house at dusk on the equinox gets direct sunlight on the west wall. At step three, tilting the Earth exposes the north wall to the sun. On the summer solstice, a house on the Tropic of Cancer gets sun on the north wall, but none on the south.
Most Chinese live north of the Tropic of Cancer. On the summer solstice, at noon, sunlight mostly hits the roof, with some slanting onto the south wall. Rotate to dusk: straighten the Earth, more sun hits the south wall; rotate to the day-night line, the west wall gets all the light; tilt, and the north wall gets sunlight.

So, even a perfectly straight house will get sunlight on its north wall in summer, even within the Arctic Circle!

From an Earth-centric view, the sun’s summer path is roughly this: rises northeast, moves diagonally, peaks south of overhead at noon, and sets northwest. This happens north and south of the Tropic of Cancer, varying only in duration.

Near the equator, things we take for granted in China are different. Singaporean real estate listings I saw didn’t indicate compass directions. Assuming north is up (a Northern Hemisphere bias), master bedrooms face every direction. We prioritize north-south orientation for sunlight, but near the equator, it’s less crucial. The sun shines on the north wall for half the year and the south wall for the other – you choose which half to keep cooler.

The Truth About Friction

hi@victor42.work (Victor42) — Wed, 20 Jan 2021 12:05:00 +0000

Friction, as taught in high school, is a simplified concept. It glosses over several underlying physical phenomena.

High school physics dictates that friction depends solely on surface roughness and the normal force. Contact area supposedly doesn’t matter.

While true in specific scenarios, this oversimplification obscures friction’s real mechanism. In reality, there’s no horizontal resistance along the contact surface. Perfectly smooth, ideal objects would experience zero friction, proving this.

Movement is actually hindered by the minuscule upward force required to lift one object over the other’s microscopic imperfections. Real-world surfaces are jagged. Two objects interlock, akin to gears (though less rigidly). Imagine the contact surface as a multitude of tiny, identical ramps. The top object rests on these ramps like a series of tiny toothpicks, similar to letterpress printing.

Moving the top object requires pushing each “toothpick” up its ramp. Once elevated, it clears the ramp’s peak. This necessitates overcoming the toothpick’s weight. Gravity and the pulling force can both be decomposed into components parallel and perpendicular to the ramp. The perpendicular components create equal and opposite reaction forces, which are irrelevant here. Only when the upward pull exceeds gravity’s downward component does movement begin. This is the essence of friction.

Therefore, friction isn’t truly independent of contact area. A larger area implies more ramps, increasing the overall normal force (N). High school physics, however, claims that changing an object’s orientation (standing vs. lying) doesn’t alter friction. This is because, while N increases, each “toothpick” shortens, reducing its weight and the downward gravitational component along the ramp. The force to move each toothpick decreases proportionally. These effects mathematically cancel out, maintaining constant friction.

However, concluding that friction is area-independent is misleading. Everyday experience confirms that larger areas do exhibit greater friction.

Two articles shed light on the true nature of friction: https://zhuanlan.zhihu.com/p/22165913 https://www.guokr.com/article/459070

Many believe fingerprints enhance grip by increasing friction. While the outcome is correct, the reasoning is flawed. Fingerprint grooves actually reduce contact area. Theoretically, a smooth finger would have a stronger grip under equal pressure. So, why fingerprints?

Fingers employ another tactic: sweat. Sweat softens the skin’s keratin, improving conformity, like interlocking gears. This creates more tiny ramps within the same area.

Excessive sweat, however, reduces friction. Wet hands struggle to open jars. An optimal moisture level exists; too much is counterproductive. Fingerprint grooves help regulate this by draining excess sweat.

Friction is ubiquitous. We spent six years in high school, solving countless problems involving blocks on various surfaces. Yet, not a single problem delved into friction’s underlying mechanism.

The Discovery of Conservation of Energy

hi@victor42.work (Victor42) — Fri, 13 Mar 2020 14:51:00 +0000

I read a fascinating story from the history of science. We’re all familiar with the conservation of energy – how it shifts between forms without being lost. But the story of its discovery is truly inspiring.

It began with mechanical energy. Consider a swing: potential energy converts to kinetic, and back again. Scientists, through experiments and calculations, found that the total energy remains constant.

Next came thermal energy. While people understood mass conservation, heat’s true nature was a mystery. One theory proposed heat as a kind of substance, massless yet capable of flowing between objects. This explained everyday observations, like mixing hot and cold water: the “heat substance” flowed, creating lukewarm water.

However, friction could generate seemingly endless heat, simply by rubbing things together. This “heat substance” appeared to materialize from nothing. This spurred investigation into the link between mechanical work and heat. Precise experiments and calculations of energy conversion finally led the scientific community to conclude that energy is conserved during mechanical-to-thermal conversions.

Around the same time, biologists suggested that animal heat and movement stemmed from food’s chemical energy. Chemists added to this, demonstrating energy conservation in chemical reactions.

Then came electromagnetism. Lenz, studying heat in current-carrying wires, found it depended on the current’s square, resistance, and time – Joule-Lenz’s law. Calculations revealed that electrical-to-thermal energy conversion is also conserved.

These discoveries occurred almost simultaneously. Different fields contributed their pieces, and when combined, revealed the true nature of energy. It was like magicians jointly casting a spell, opening a portal to a dazzling new world.