Theory of navigation. Division of the true horizon and distance of the visible horizon. How far can the human eye see? Formulas for calculating lightning visibility distance

The surface of the Earth in your field of view begins to curve at a distance of about 5 km. But the acuity of human vision allows us to see much further than the horizon. If there was no curvature, you would be able to see the flame of a candle 50 km away.

The range of vision depends on the number of photons emitted by a distant object. This galaxy's 1,000,000,000,000 stars collectively emit enough light for several thousand photons to reach every square meter. cm Earth. This is enough to excite the retina of the human eye.

Since it is impossible to check the acuity of human vision while on Earth, scientists resorted to mathematical calculations. They found that in order to see flickering light, between 5 and 14 photons need to hit the retina. A candle flame at a distance of 50 km, taking into account the scattering of light, gives this amount, and the brain recognizes a weak glow.

How to find out something personal about the interlocutor by his appearance

Secrets of “owls” that “larks” don’t know about

How does “brainmail” work - transmitting messages from brain to brain via the Internet

Why is boredom necessary?

“Man Magnet”: How to become more charismatic and attract people to you

25 Quotes That Will Bring Out Your Inner Fighter

5 Reasons People Will Always Blame the Victim, Not the Criminal, for a Crime

Experiment: a man drinks 10 cans of cola a day to prove its harm

The geographic range of visibility of objects in the sea D p is determined by the greatest distance at which the observer will see its top above the horizon, i.e. depends only on geometric factors connecting the height of the observer’s eye e and the height of the landmark h at the refractive index c (Fig. 1.42):

where D e and D h are the distances of the visible horizon from the height of the observer’s eye and the height of the object, respectively. That. the visibility range of an object calculated from the height of the observer’s eye and the height of the object is called geographic or geometric visibility range.

Calculation of the geographic range of visibility of an object can be made using the table. 2.3 MT – 2000 according to arguments e and h or according to table. 2.1 MT – 2000 by summing the results obtained by entering the table twice using arguments e and h. You can also obtain Dp using the Struisky nomogram, which is given in MT - 2000 under number 2.4, as well as in each book “Lights” and “Lights and Signs” (Fig. 1.43).

On marine navigation charts and in navigation manuals, the geographic range of visibility of landmarks is given for a constant height of the observer’s eye e = 5 m and is designated as D k - the visibility range indicated on the map.

Substituting the value e = 5 m into formula (1.126), we obtain:

To determine D p it is necessary to introduce a correction D D to D k, the value and sign of which are determined by the formula:

If the actual height of the eye is more than 5 m, then DD has a “+” sign, if less - a “-“ sign. Thus:

. (1.129)

The value of Dp also depends on visual acuity, which is expressed in the angular resolution of the eye, i.e. is also determined by the smallest angle at which the object and the horizon line are distinguished separately (Fig. 1.44).

In accordance with formula (1.126)

But due to the resolution of the eye g, the observer will see an object only when its angular dimensions are not less than g, i.e. when it is visible above the horizon line by at least Dh, which from the elementary DA¢CC¢ at angles C and C¢ close to 90° will be Dh = D p × g¢.

To get D p g in miles with Dh in meters:

where D p g is the geographic range of visibility of an object, taking into account the resolution of the eye.

Practical observations have determined that when the beacon is opened, g = 2¢, and when hidden, g = 1.5¢.

Example. Find the geographic range of visibility of a lighthouse with a height of h = 39 m, if the height of the observer’s eye is e = 9 m, without and taking into account the resolution of the eye g = 1.5¢.

Influence of hydrometeorological factors on the visibility range of lights

In addition to geometric factors (e and h), the visibility range of landmarks is also influenced by contrast, which allows the landmark to be distinguished from the surrounding background.

The visibility range of landmarks during the day, which also takes into account contrast, is called daytime optical visibility range.

To ensure safe navigation at night, special navigation equipment with light-optical devices is used: beacons, illuminated navigation signs and navigation lights.

Sea lighthouse - This is a special permanent structure with a visibility range of white or colored lights associated with it of at least 10 miles.

Glowing marine navigation sign- a capital structure that has a light-optical apparatus with a visibility range of white or colored lights reduced to it less than 10 miles.

Marine navigation light- a lighting device installed on natural objects or structures of non-special construction. Such aids to navigation often operate automatically.

IN dark time day, the visibility range of lighthouse lights and luminous navigational signs depends not only on the height of the observer’s eye and the height of the luminous aid to navigation, but also on the strength of the light source, the color of the fire, the design of the light-optical apparatus, as well as on the transparency of the atmosphere.

The visibility range that takes into account all these factors is called night optical visibility range, those. this is the maximum visibility range of the fire at a given time for a given meteorological visibility range.

Meteorological visibility range depends on the transparency of the atmosphere. Part of the luminous flux of lights of illuminated aids to navigation is absorbed by particles contained in the air, therefore, a weakening of the luminous intensity occurs, characterized by atmospheric transparency coefficient t:

where I 0 is the light intensity of the source; I 1 - luminous intensity at a certain distance from the source, taken as a unit (1 km, 1 mile).

The atmospheric transparency coefficient is always less than unity, so the geographic visibility range is usually greater than the actual one, except in anomalous cases.

The transparency of the atmosphere in points is assessed according to the visibility scale of table 5.20 MT - 2000 depending on the state of the atmosphere: rain, fog, snow, haze, etc.

Since the optical range of lights varies greatly depending on the transparency of the atmosphere, the International Association of Lighthouse Authorities (IALA) has recommended the use of the term “nominal range”.

Nominal fire visibility range is called the optical visibility range at a meteorological visibility range of 10 miles, which corresponds to the atmospheric transparency coefficient t = 0.74. The nominal visibility range is indicated in navigation manuals of many foreign countries. Domestic maps and navigation manuals indicate the standard visibility range (if it is less than the geographic visibility range).

Standard visibility range The fire is called the optical visibility range with a meteorological visibility range of 13.5 miles, which corresponds to the atmospheric transparency coefficient t = 0.8.

In the navigation manuals “Lights”, “Lights and Signs”, in addition to the table of the range of the visible horizon and the nomogram of the range of visibility of objects, there is also a nomogram of the optical range of visibility of lights (Fig. 1.45). The same nomogram is given in MT - 2000 under number 2.5.

The inputs to the nomogram are luminous intensity, or nominal or standard visual range, (obtained from navigation aids), and meteorological visual range, (obtained from the meteorological forecast). Using these arguments, the optical range of visibility is obtained from the nomogram.

When designing beacons and lights, they strive to ensure that the optical visibility range is equal to the geographic visibility range in clear weather. However, for many lights the optical visibility range is less than the geographic range. If these ranges are not equal, then the smaller of them is indicated on charts and in navigation manuals.

For practical calculations of the expected fire visibility range during the day It is necessary to calculate D p using the formula (1.126) based on the heights of the observer’s eye and the landmark. At night: a) if the optical visibility range is greater than the geographic one, it is necessary to take a correction for the height of the observer’s eye and calculate the geographic visibility range using formulas (1.128) and (1.129). Accept the smaller of the optical and geographical calculated using these formulas; b) if the optical visibility range is less than the geographical one, accept the optical range.

If on the map there is a fire or lighthouse D k< 2,1 h + 4,7 , то поправку DД вводить не нужно, т.к. эта дальность видимости оптическая меньшая географической дальности видимости.

Example. The height of the observer's eye is e = 11 m, the visibility range of the fire indicated on the map is D k = 16 miles. The nominal visibility range of the lighthouse from the navigation manual “Lights” is 14 miles. Meteorological visibility range 17 miles. At what distance can we expect the lighthouse to fire?

According to the nomogram Dopt » 19.5 miles.

By e = 11m ® D e = 6.9 miles

D 5 = 4.7 miles

DD =+2.2 miles

D k = 16.0 miles

D n = 18.2 miles

Answer: You can expect to open fire from a distance of 18.2 miles.

Nautical charts. Map projections. Transverse equiangular cylindrical Gaussian projection and its use in navigation. Perspective projections: stereographic, gnomonic.

A map is a reduced distorted image of the spherical surface of the Earth on a plane, provided that the distortions are natural.

A plan is an image of the earth’s surface on a plane, not distorted due to the smallness of the depicted area.

A cartographic grid is a set of lines depicting meridians and parallels on a map.

Map projection is a mathematically based way of depicting meridians and parallels.

A geographic map is a conventional image of the entire earth's surface or part of it constructed in a given projection.

Maps vary in purpose and scale, for example: planispheres - depicting the entire Earth or hemisphere, general or general - depicting individual countries, oceans and seas, private - depicting smaller spaces, topographic - depicting details of the land surface, orographic - relief maps, geological - occurrence of layers, etc.

Nautical charts are special geographic maps designed primarily to support navigation. In the general classification of geographic maps, they are classified as technical. A special place among nautical charts is occupied by MNCs, which are used to plot the course of a ship and determine its place in the sea. A ship's collection may also contain auxiliary and reference charts.

Classification of map projections.

According to the nature of distortions, all cartographic projections are divided into:

• Conformal or conformal - projections in which the figures on the maps are similar to the corresponding figures on the surface of the Earth, but their areas are not proportional. The angles between objects on the ground correspond to those on the map.
• Equal or equivalent - in which the proportionality of the areas of the figures is preserved, but at the same time the angles between the objects are distorted.
• Equidistant - preserving the length along one of the main directions of the ellipse of distortions, i.e., for example, a circle on the ground on a map is depicted as an ellipse in which one of the semi-axes is equal to the radius of such a circle.
• Arbitrary - all others that do not have the above properties, but are subject to other conditions.

Based on the method of constructing projections, they are divided into:

Depending on the point of contact of the picture plane, gnomonic projections are divided into: normal or polar - touching at one of the poles transverse or equatorial - touching at the equator
horizontal or oblique - touching at any point between the pole and the equator (meridians on the map in such a projection are rays diverging from the pole, and parallels are ellipses, hyperbolas or parabolas.

Question No. 10.

Distance of the visible horizon. Object visibility range...

Geographic horizon visibility range

Let the height of the eye of the observer located at the point A" above sea level, equal to e(Fig. 1.15). surface of the Earth in the form of a sphere with radius R

The rays of sight going to A" and tangent to the surface of the water in all directions form a small circle KK", which is called theoretically visible horizon line.

Due to the different density of the atmosphere in height, a ray of light does not propagate rectilinearly, but along a certain curve A"B, which can be approximated by a circle with radius ρ .

The phenomenon of curvature of the visual ray in the Earth's atmosphere is called terrestrial refraction and usually increases the range of the theoretically visible horizon. the observer sees not KK", but the line BB", which is a small circle along which the surface of the water touches the sky. This observer's apparent horizon.

The coefficient of terrestrial refraction is calculated using the formula. Its average value:

Refractive angler determined, as shown in the figure, by the angle between the chord and the tangent to the circle of radiusρ .

The spherical radius A"B is called geographical or geometric range of the visible horizon De. This visibility range does not take into account the transparency of the atmosphere, i.e. it is assumed that the atmosphere is ideal with a transparency coefficient m = 1.

Let us draw the plane of the true horizon H through point A", then the vertical angle d between H and the tangent to the visual ray A"B will be called horizon inclination

In the MT-75 Nautical Tables there is a table. 22 “Range of the visible horizon”, calculated using formula (1.19).

Geographic visibility range of objects

Geographic range of visibility of objects at sea Dp, as follows from the previous paragraph, will depend on the value e- height of the observer’s eye, magnitude h- the height of the object and the refractive index X.

The value of Dp is determined by the greatest distance at which the observer will see its top above the horizon line. In professional terminology, there is the concept of range, as well as moments"open" And"closing" a navigational landmark, such as a lighthouse or ship. Calculation of such a range allows the navigator to have additional information about the approximate position of the ship relative to the landmark.

where Dh is the visibility range of the horizon from the height of the object

On marine navigation charts, the geographic visibility range of navigation landmarks is given for the height of the observer's eye e = 5 m and is designated as Dk - the visibility range indicated on the map. In accordance with (1.22), it is calculated as follows:

Accordingly, if e differs from 5 m, then to calculate Dp to the visibility range on the map, an amendment is necessary, which can be calculated as follows:

There is no doubt that Dp depends on the physiological characteristics of the observer’s eye, on visual acuity, expressed in resolution at.

Angle resolution- this is the smallest angle at which two objects are distinguished by the eye as separate, i.e. in our task it is the ability to distinguish between an object and the horizon line.

Let's look at Fig. 1.18. Let us write down the formal equality

Due to the resolution of the object, an object will be visible only if its angular dimensions are no less than at, i.e. it will have a height above the horizon line of at least SS". Obviously, y should reduce the range, calculated using formulas (1.22). Then

The segment CC" actually reduces the height of object A.

Assuming that in ∆A"CC" angles C and C" are close to 90°, we find

If we want to get Dp y in miles, and SS" in meters, then the formula for calculating the visibility range of an object, taking into account the resolution of the human eye, must be reduced to the form

The influence of hydrometeorological factors on the visibility range of the horizon, objects and lights

The visibility range can be interpreted as an a priori range without taking into account the current transparency of the atmosphere, as well as the contrast of the object and background.

Optical visibility range- this is the range of visibility, depending on the ability of the human eye to distinguish an object by its brightness against a certain background, or, as they say, to distinguish a certain contrast.

Daytime optical visibility range depends on the contrast between the observed object and the background of the area. Daytime optical visibility range represents the greatest distance at which the apparent contrast between the object and the background becomes equal to the threshold contrast.

Night optical visibility range this is the maximum visibility range of the fire at a given time, determined by the intensity of the light and the current meteorological visibility.

Contrast K can be defined as follows:

Where Vf is the background brightness; Bp is the brightness of the object.

The minimum value of K is called threshold of contrast sensitivity of the eye and equals on average 0.02 for daytime conditions and objects with angular dimensions of about 0.5°.

Part of the luminous flux from lighthouse lights is absorbed by particles in the air, resulting in a weakening of the light intensity. This is characterized by the atmospheric transparency coefficient

Where I0 - luminous intensity of the source; /1 - luminous intensity at a certain distance from the source, taken as unity.

TO the atmospheric transparency coefficient is always less than unity, which means geographical range- this is the theoretical maximum, which in real conditions the visibility range does not reach, with the exception of anomalous cases.

Atmospheric transparency can be assessed in points using a visibility scale from table 51 MT-75 depending on the state of the atmosphere: rain, fog, snow, haze, etc.

Thus, the concept arises meteorological visibility range, which depends on the transparency of the atmosphere.

Nominal visibility range fire is called the optical visibility range with a meteorological visibility range of 10 miles (ד = 0.74).

The term is recommended by the International Association of Lighthouse Authorities (IALA) and is used abroad. On domestic maps and in navigation manuals, the standard visibility range is indicated (if it is less than the geographical one).

Standard visibility range- this is the optical range with meteorological visibility of 13.5 miles (ד = 0.80).

The navigation manuals “Lights” and “Lights and Signs” contain a table of horizon visibility range, a nomogram of object visibility and a nomogram of optical visibility range. The nomogram can be entered by luminous intensity in candelas, by nominal (standard) range and by meteorological visibility, resulting in the optical range of visibility of the fire (Fig. 1.19).

The navigator must experimentally accumulate information about the opening ranges of specific lights and signs in the navigation area in various weather conditions.

Chapter VII. Navigation.

Navigation is the basis of the science of navigation. The navigational method of navigation is to navigate a ship from one place to another in the most advantageous, shortest and safest way. This method solves two problems: how to direct the ship along the chosen path and how to determine its place in the sea based on the elements of the ship’s movement and observations of coastal objects, taking into account the influence of external forces on the ship - wind and current.

To be sure of the safe movement of your ship, you need to know the ship’s place on the map, which determines its position relative to the dangers in a given navigation area.

Navigation deals with the development of the fundamentals of navigation, it studies:

Dimensions and surface of the earth, methods of depicting the earth's surface on maps;

Methods for calculating and plotting a ship's path on nautical charts;

Methods for determining the position of a ship at sea by coastal objects.

§ 19. Basic information about navigation.

1. Basic points, circles, lines and planes

Our earth has the shape of a spheroid with a semi-major axis OE equal to 6378 km, and the minor axis OR 6356 km(Fig. 37).

Rice. 37. Determining the coordinates of a point on the earth's surface

In practice, with some assumption, the earth can be considered a ball rotating around an axis occupying a certain position in space.

To determine points on the earth's surface, it is customary to mentally divide it into vertical and horizontal planes that form lines with the earth's surface - meridians and parallels. The ends of the earth's imaginary axis of rotation are called poles - north, or north, and south, or south.

Meridians are large circles passing through both poles. Parallels are small circles on the earth's surface parallel to the equator.

Equator - big circle, the plane of which passes through the center of the earth perpendicular to its axis of rotation.

Both meridians and parallels on the earth's surface can be imagined in countless numbers. The equator, meridians and parallels form the earth's geographic coordinate grid.

Location of any point A on the earth's surface can be determined by its latitude (f) and longitude (l) .

The latitude of a place is the arc of the meridian from the equator to the parallel of a given place. Otherwise: the latitude of a place is measured by the central angle between the plane of the equator and the direction from the center of the earth to a given place. Latitude is measured in degrees from 0 to 90° in the direction from the equator to the poles. When calculating, it is assumed that northern latitude f N has a plus sign, southern latitude f S has a minus sign.

The latitude difference (f 1 - f 2) is the meridian arc enclosed between the parallels of these points (1 and 2).

The longitude of a place is the arc of the equator from the prime meridian to the meridian of a given place. Otherwise: the longitude of a place is measured by the arc of the equator, enclosed between the plane of the prime meridian and the plane of the meridian of a given place.

The difference in longitude (l 1 -l 2) is the arc of the equator, enclosed between the meridians of given points (1 and 2).

The prime meridian is the Greenwich meridian. From it, longitude is measured in both directions (east and west) from 0 to 180°. Western longitude is measured on the map to the left of the Greenwich meridian and is taken with a minus sign in calculations; eastern - to the right and has a plus sign.

The latitude and longitude of any point on earth are called the geographic coordinates of that point.

2. Division of the true horizon

A mentally imaginary horizontal plane passing through the observer’s eye is called the plane of the observer’s true horizon, or true horizon (Fig. 38).

Let us assume that at the point A is the observer's eye, line ZABC- vertical, HH 1 - the plane of the true horizon, and line P NP S - the axis of rotation of the earth.

Of the many vertical planes, only one plane in the drawing will coincide with the axis of rotation of the earth and the point A. The intersection of this vertical plane with the surface of the earth gives on it a great circle P N BEP SQ, called the true meridian of the place, or the meridian of the observer. The plane of the true meridian intersects with the plane of the true horizon and gives the north-south line on the latter N.S. Line O.W. perpendicular to the line of true north-south is called the line of true east and west (east and west).

Thus, the four main points of the true horizon - north, south, east and west - occupy a well-defined position anywhere on earth, except for the poles, thanks to which different directions along the horizon can be determined relative to these points.

Directions N(north), S (south), ABOUT(East), W(west) are called the main directions. The entire circumference of the horizon is divided into 360°. Division is made from the point N in a clockwise direction.

Intermediate directions between the main directions are called quarter directions and are called NO, SO, SW, NW. The main and quarter directions have the following values ​​in degrees:

Rice. 38. Observer's true horizon

3. Visible horizon, visible horizon range

The expanse of water visible from a vessel is limited by a circle formed by the apparent intersection of the vault of heaven with the surface of the water. This circle is called the observer's apparent horizon. The range of the visible horizon depends not only on the height of the observer’s eyes above the water surface, but also on the state of the atmosphere.

Figure 39. Object visibility range

The boatmaster should always know how far he can see the horizon in different positions, for example, standing at the helm, on deck, sitting, etc.

The range of the visible horizon is determined by the formula:

d = 2.08

or, approximately, for an observer's eye height of less than 20 m by formula:

d = 2,

where d is the range of the visible horizon in miles;

h is the height of the observer's eye, m.

Example. If the height of the observer's eye is h = 4 m, then the range of the visible horizon is 4 miles.

The visibility range of the observed object (Fig. 39), or, as it is called, the geographic range D n , is the sum of the ranges of the visible horizon With the height of this object H and the height of the observer’s eye A.

Observer A (Fig. 39), located at a height h, from his ship can see the horizon only at a distance d 1, i.e. to point B of the water surface. If we place an observer at point B of the water surface, then he could see lighthouse C , located at a distance d 2 from it ; therefore the observer located at the point A, will see the beacon from a distance equal to D n :

D n= d 1+d 2.

The visibility range of objects located above the water level can be determined by the formula:

Dn = 2.08(+).

Example. Lighthouse height H = 1b.8 m, observer's eye height h = 4 m.

Solution. D n = l 2.6 miles, or 23.3 km.

The visibility range of an object is also determined approximately using the Struisky nomogram (Fig. 40). By applying a ruler so that one straight line connects the heights corresponding to the observer’s eye and the observed object, the visibility range is obtained on the middle scale.

Example. Find the visibility range of an object with an altitude of 26.2 above sea level m with an observer's eye height above sea level of 4.5 m.

Solution. Dn= 15.1 miles (dashed line in Fig. 40).

On maps, directions, in navigation manuals, in the descriptions of signs and lights, the visibility range is given for the height of the observer's eye 5 m from the water level. Since on a small boat the observer’s eye is located below 5 m, for him, the visibility range will be less than that indicated in manuals or on the map (see Table 1).

Example. The map indicates the visibility range of the lighthouse at 16 miles. This means that an observer will see this lighthouse from a distance of 16 miles if his eye is at a height of 5 m above sea level. If the observer's eye is at a height of 3 m, then the visibility will correspondingly decrease by the difference in the horizon visibility range for heights 5 and 3 m. Horizon visibility range for height 5 m equal to 4.7 miles; for height 3 m- 3.6 miles, difference 4.7 - 3.6=1.1 miles.

Consequently, the visibility range of the lighthouse will not be 16 miles, but only 16 - 1.1 = 14.9 miles.

Rice. 40. Struisky's nomogram

Talks about amazing properties our vision - from the ability to see distant galaxies to the ability to capture seemingly invisible light waves.

Look around the room you are in - what do you see? Walls, windows, colorful objects - all this seems so familiar and taken for granted. It's easy to forget that we see the world around us only thanks to photons - light particles reflected from objects and striking the retina.

There are approximately 126 million light-sensitive cells in the retina of each of our eyes. The brain deciphers the information received from these cells about the direction and energy of photons falling on them and turns it into a variety of shapes, colors and intensity of illumination of surrounding objects.

Human vision has its limits. Thus, we are neither able to see radio waves emitted by electronic devices, nor to see the smallest bacteria with the naked eye.

Thanks to advances in physics and biology, the limits of natural vision can be determined. "Every object we see has a certain 'threshold' below which we stop recognizing them," says Michael Landy, a professor of psychology and neurobiology at New York University.

Let's first consider this threshold in terms of our ability to distinguish colors - perhaps the very first ability that comes to mind in relation to vision.

Our ability to distinguish, e.g. purple from magenta is related to the wavelength of photons striking the retina. There are two types of light-sensitive cells in the retina - rods and cones. Cones are responsible for color perception (so-called day vision), and rods allow us to see shades of gray in low light - for example, at night (night vision).

The human eye has three types of cones and a corresponding number of types of opsins, each of which is particularly sensitive to photons with a specific range of light wavelengths.

S-type cones are sensitive to the violet-blue, short-wavelength portion of the visible spectrum; M-type cones are responsible for green-yellow (medium wavelength), and L-type cones are responsible for yellow-red (long wavelength).

All of these waves, as well as their combinations, allow us to see the full range of colors of the rainbow. "All sources visible to humans"lights, with the exception of some artificial ones (such as a refractive prism or laser), emit a mixture of wavelengths of different lengths," says Landy.

Of all the photons existing in nature, our cones are capable of detecting only those characterized by wavelengths in a very narrow range (usually from 380 to 720 nanometers) - this is called the visible radiation spectrum. Below this range are the infrared and radio spectra - the wavelengths of the latter's low-energy photons vary from millimeters to several kilometers.

On the other side of the visible wavelength range is the ultraviolet spectrum, followed by X-rays, and then the gamma ray spectrum with photons whose wavelengths are less than trillionths of a meter.

Although most of us have limited vision in the visible spectrum, people with aphakia - the absence of a lens in the eye (resulting surgery with cataracts or, less commonly, due to birth defect) - are able to see ultraviolet waves.

In a healthy eye, the lens blocks ultraviolet waves, but in its absence, a person is able to perceive waves up to about 300 nanometers in length as blue-white color.

A 2014 study notes that, in some sense, we can all see infrared photons. If two such photons hit the same retinal cell almost simultaneously, their energy can add up, turning invisible waves of, say, 1000 nanometers in length into visible wave 500 nanometers long (most of us perceive waves of this length as a cool green color).

How many colors do we see?

In the eye healthy person three types of cones, each of which is capable of distinguishing about 100 different shades of color. For this reason, most researchers estimate the number of colors we can distinguish at about a million. However, color perception is very subjective and individual.

Jameson knows what he's talking about. She studies the vision of tetrachromats - people with truly superhuman abilities to distinguish colors. Tetrachromacy is rare and occurs in most cases in women. As a result of a genetic mutation, they have an additional, fourth type of cone, which allows them, according to rough estimates, to see up to 100 million colors. (In people suffering color blindness, or dichromats, there are only two types of cones - they distinguish no more than 10,000 colors.)

How many photons do we need to see a light source?

In general, cones require much more light to function optimally than rods. For this reason, in low light, our ability to distinguish colors decreases, and rods are taken to work, providing black and white vision.

Under ideal laboratory conditions, in areas of the retina where rods are largely absent, cones can be activated by just a few photons. However, the wands do an even better job of registering even the dimmest light.

As experiments first conducted in the 1940s show, one quantum of light is enough for our eyes to see it. "A person can see a single photon," says Brian Wandell, a professor of psychology and electrical engineering at Stanford University. "It just doesn't make sense for the retina to be more sensitive."

In 1941, researchers from Columbia University conducted an experiment - they took subjects into a dark room and gave their eyes a certain time to adapt. The rods require several minutes to achieve full sensitivity; This is why when we turn off the lights in a room, we lose the ability to see anything for a while.

A flashing blue-green light was then directed at the subjects' faces. With a probability higher than ordinary chance, the experiment participants recorded a flash of light when only 54 photons hit the retina.

Not all photons reaching the retina are detected by light-sensitive cells. Taking this into account, scientists have come to the conclusion that just five photons activating five different rods in the retina are enough for a person to see a flash.

Smallest and most distant visible objects

The following fact may surprise you: our ability to see an object does not depend at all on its physical size or distance, but on whether at least a few photons emitted by it will hit our retina.

“The only thing the eye needs to see something is a certain amount of light emitted or reflected by the object,” says Landy. “It all comes down to the number of photons that reach the retina. No matter how small the light source, even if it exists for a fraction of a second, we can still see it if it emits enough photons."

Psychology textbooks often contain the statement that on a cloudless, dark night, a candle flame can be seen from a distance of up to 48 km. In reality, our retina is constantly bombarded by photons, so that a single quantum of light emitted from a great distance is simply lost against their background.

To get an idea of ​​how far we can see, let's look at the night sky, dotted with stars. The size of the stars is enormous; many of those we see with the naked eye reach millions of kilometers in diameter.

However, even the stars closest to us are located at a distance of over 38 trillion kilometers from Earth, so their apparent sizes are so small that our eyes are not able to distinguish them.

On the other hand, we still observe stars in the form of bright point sources of light, since the photons emitted by them overcome the gigantic distances separating us and land on our retina.

All individual visible stars in the night sky are located in our galaxy, the Milky Way. The most distant object from us that a person can see with the naked eye is located outside the Milky Way and is itself a star cluster - this is the Andromeda Nebula, located at a distance of 2.5 million light years, or 37 quintillion km, from the Sun. (Some people claim that on particularly dark nights, their keen vision allows them to see the Triangulum Galaxy, located about 3 million light years away, but leave this claim to their conscience.)

The Andromeda nebula contains one trillion stars. Due to the great distance, all these luminaries merge for us into a barely visible speck of light. Moreover, the size of the Andromeda Nebula is colossal. Even at such a gigantic distance, its angular size is six times the diameter full moon. However, so few photons from this galaxy reach us that it is barely visible in the night sky.

Visual acuity limit

Why are we unable to see individual stars in the Andromeda Nebula? The fact is that resolution, or visual acuity, has its limitations. (Visual acuity refers to the ability to distinguish elements such as a point or line as separate objects that do not blend into adjacent objects or the background.)

In fact, visual acuity can be described in the same way as the resolution of a computer monitor - in the minimum size of pixels that we are still able to distinguish as individual points.

Limitations in visual acuity depend on several factors, such as the distance between the individual cones and rods of the retina. An equally important role is played by the optical characteristics of the eyeball, due to which not every photon hits the light-sensitive cell.

In theory, research shows that our visual acuity is limited to the ability to distinguish about 120 pixels per angular degree (a unit of angular measurement).

A practical illustration of the limits of human visual acuity can be an object located at arm's length, the size of a fingernail, with 60 horizontal and 60 vertical lines of alternate white and black colors applied to it, forming a semblance of a chessboard. "Apparently, this is the smallest pattern that can still be distinguished human eye"Landy says.

The tables used by ophthalmologists to test visual acuity are based on this principle. The most famous table in Russia, Sivtsev, consists of rows of black capital letters on a white background, the font size of which becomes smaller with each row.

A person’s visual acuity is determined by the size of the font at which he ceases to clearly see the outlines of letters and begins to confuse them.

It is the limit of visual acuity that explains the fact that we are not able to see with the naked eye biological cell, the dimensions of which are only a few micrometers.

But there is no need to grieve over this. The ability to distinguish a million colors, capture single photons and see galaxies several quintillion kilometers away is quite a good result, considering that our vision is provided by a pair of jelly-like balls in the eye sockets, connected to a 1.5 kg porous mass in the skull.