Today we will tell you all about the illumination formula for open areas and premises, and also give the magnitude of the light flux under different circumstances.
Candle and spinning wheel
Before the widespread electrification, the light source was the sun, moon, bonfire and candle. Scientists already in the fifteenth century were able to create a lens system to enhance illumination, but most people worked and lived by candlelight.
Some were sorry to spend money on wax sources of light, or this way to extend the day was simply not available. Then used alternative fuel options - oil, animal fat, wood. For example, Russian middle-class peasant women all their lives weaved linen in the light of a torch. The reader may ask: “Why did you have to do this at night?” After all, the coefficient of natural daylight is much higher. The fact is that in the daytime the peasants had many other concerns. In addition, the weaving process is very painstaking and requires peace of mind. It was important for women that no one stepped on the canvas, that children did not confuse the threads, and men did not distract.
But with such a life, there is one danger: the luminous flux (we give the formula below) from the torch is very low. Eyes were strained, and women quickly lost their sight.
Lighting and training
When first graders go to school on September 1, they anxiously expect miracles. They are captured by a ruler, flowers, beautiful shape. They are interested in what their teacher will be, with whom they will sit at the same desk. And a person remembers these feelings for life.
But adults, when they send their children to school, should think about more prosaic things than delight or disappointment. Parents and teachers care about the convenience of the school desk, the size of the classroom, the quality of the chalk and the formula for lighting the room. These indicators have norms for children of all ages. Therefore, schoolchildren should be grateful that people thought in advance not only the curriculum, but also the material side of the issue.
Lighting and work
It is not without reason that inspections are carried out in schools that use the formula for calculating the illumination of classrooms. Children of ten or eleven years old only do what they read and write. Then they do their homework in the evening, again without parting with pens, notebooks and textbooks. After that, modern teens also stumble into a variety of screens. As a result, the whole life of a student is associated with a load on his eyesight. But school is only the beginning of a life journey. The university and labor are waiting for all these people.
Each type of work requires its own luminous flux. The calculation formula always takes into account what a person does 8 hours a day. For example, a watchmaker or jeweler should consider the smallest details and shades of colors. Therefore, the workplace of people in this profession requires large and bright lamps. A botanist who studies the plants of the rainforest, on the contrary, must constantly be in the twilight. Orchids and bromeliads are used to the fact that the upper tier of trees selects almost all the sunlight.
Formula
We come directly to the formula for illumination. Her mathematical expression looks like this:
E υ = dΦ υ / dσ.
Let's take a closer look at the expression. Obviously, E υ is the illumination, then Φ υ is the luminous flux, and σ is the small unit of the area onto which the flux falls. It can be seen that E is an integral quantity. This means that very small segments and pieces are considered. That is, scientists summarize the illumination of all these small areas to get the final result. The unit of illumination is lux. The physical meaning of one lux is such a luminous flux, for which one lumen falls on one square meter. Lumen, in turn, is a very specific quantity. It denotes the luminous flux that emits a point isotropic source (therefore, the light is monochromatic). The luminous intensity of this source is equal to one candela at a solid angle of one steradian. The unit of illumination is a complex quantity that includes the concept of "candela." The physical meaning of the latter definition is as follows: the light intensity in a known direction from a source that emits monochromatic radiation with a frequency of 540 · 10 12 Hz (the wavelength lies in the visible region of the spectrum), and the energy intensity of light is 1/683 W / sr.
Lighting Concepts
Of course, all these concepts at first glance look like a spherical horse in a vacuum. Such sources do not exist in nature. And the attentive reader will certainly ask himself the question: “Why is this needed?” But physicists have a need to compare. Therefore, they have to introduce certain norms that need to be guided. The formula for illumination is simple, but much can be incomprehensible. We will reveal this in more detail.
Υ index
Index υ means that the value is not quite photometric. And this is due to the fact that human capabilities are limited. For example, the eye perceives only the visible spectrum of electromagnetic radiation. Moreover, the central part of this scale (refers to green) people see much better than the edge areas (red and purple). That is, in fact, a person does not perceive 100% of photons yellow or blue. Moreover, there are devices devoid of such an error. The reduced values that the illumination formula operates on (luminous flux, for example) and which are indicated by the Greek letter "υ", are corrected for human vision.
Monochromatic radiation generator
At the very core, as mentioned above, is the number of photons with a certain wavelength that are emitted in a certain direction per unit time. Even the most monochromatic laser has some wavelength distribution. And certainly he should hold on to something. This means that photons are not emitted in all directions. But in the formula appears such a thing as a "point source of light." This is another model designed to unify a certain value. And not a single object of the universe can be so called. So, a point light source is a photon generator that emits an equal number of electromagnetic field quanta in all directions, its size is equal to a mathematical point. However, there is one trick, it can make a real object a point source: if the distance over which the photons fly is very large compared to the size of the generator. Thus, our central star, the Sun, is a disk, but distant stars are points.
Garden furniture, well, park
Surely an attentive reader noticed the following: on a bright sunny day, the open area seems to be much more illuminated than a glade or lawn closed on one side. Therefore, the seashore beckons: it is always sunny and warm. But even a large clearing in the forest is darker and colder. And a shallow well is poorly lit on the brightest day. This is because if a person sees only part of the sky, fewer photons reach his eye. The coefficient of natural illumination is calculated as the ratio of the light flux from the entire sky to the visible area.
Circle, oval, corner
All of these concepts are related to geometry. But now we will talk about a phenomenon that directly relates to the formula of illumination and, therefore, to physics. Up to this point, it was assumed that light falls on the surface perpendicularly, strictly down. This, of course, is also an approximation. If this condition is met, moving away from the light source means a drop in illumination in proportion to the square of the distance. Thus, the stars that a person sees with the naked eye in the sky are either located not so far from us (they all belong to the Milky Way galaxy) or are very bright. But if light hits the surface at an angle, everything is different.
Imagine a flashlight. It gives a round spot of light when directed strictly perpendicular to the wall. If you tilt it, the spot will change its shape to an oval. As is known from geometry, the oval has a larger area. And since the flashlight is still the same, it means that the light intensity is the same, but it is as if "spread out" over a large area. The light intensity depends on the angle of incidence according to the law of cosine.
Spring, winter, fall
The title sounds like the name of a beautiful movie. But the presence of seasons directly depends on the angle at which light falls at its highest point on the surface of the planet. And at the moment it is not only about the Earth. Seasons exist on any object in the solar system whose rotation axis is inclined with respect to the ecliptic (for example, on Mars). The reader probably already guessed: the greater the angle of inclination, the fewer photons per square kilometer of surface per second. So, the colder the season will be. At the time of the largest deviation of the planet in the hemisphere, winter reigns, at the time of the smallest - summer.
Facts and Figures
In order not to be unfounded, we give some data. We warn you: they are all averaged and are not suitable for solving specific problems. In addition, there are directories of illuminance of surfaces by different types of sources. It is better to contact them when making calculations.
- At a distance from the Sun to any point in space that is approximately equal to the distance to the Earth, the illumination is one hundred and thirty-five thousand lux.
- Our planet has an atmosphere that absorbs part of the radiation. Therefore, the surface of the earth is lit up to a maximum of one hundred thousand lux.
- In summer, mid-latitudes at noon are illuminated by seventeen thousand lux in clear weather and by fifteen thousand lux in cloudy weather.
- At night on a full moon, illumination is two tenths of a lux. The light of stars on a moonless night gives only one or two thousandths of a suite.
- To read a book you need at least thirty to fifty lux illumination.
- When a person watches a movie in a movie theater, the luminous flux is about a hundred lux. The darkest scenes will have an indicator of eighty lux, and the image of a bright sunny day will "pull" one hundred and twenty.
- Sunset or sunrise over the sea will give illumination of about one thousand lux. At the same time, at a depth of fifty meters, the illumination will be about 20 lux. Water absorbs sunlight very well.