So im reading some Ex Soviet book (form 60s, so take into account that there was no zoom type lenses) regarding Photography. As i could not find more or less comprehensive and simple explanation of aperture and focal lenght on internet (most probably it is) i decided to translate (of course google helped) few pieces where is quite good explained how the lense works. Of course in the books are named soviet cameras and soviet lenses but bear with me.
Focal lengt (Main focal Lengt)
If you direct a beam of light rays parallel to the main optical axis of the lens onto a converging (for example, biconvex) lens, as shown in Fig. 7, in the upper left corner, then after refraction in the lens these rays will converge at the main focus. The distance from the lens to the main focus is the main focal length of the lens.
To a reasonable approximation, it can be determined by placing a lens or objective in the path of the sun's rays, which are practically parallel, and obtaining a sharp image of the sun on paper. The distance between the lens and the paper will be the main focal length of the lens. It can be measured with a ruler.
Why is this distance called the main one?
Using a lens, you can notice that as the distance between the object and the lens changes, the distance from the lens to the image of the object also changes.
Let's do the following experiment. Let us take a biconvex lens and a sheet of white paper and, placing the lens at a short distance from a burning lamp, we will obtain a sharp image of the lamp on the paper. After measuring the distance between the lens and the paper, we will begin to move further away from the lamp, maintaining the sharpness of the image. It is easy to see that the distance between the lens and paper will first decrease rather quickly, and then more slowly, as if fading, and finally the moment will come when it will stop shortening. And no matter how far we move from the lamp, the distance from the lens to the paper will practically not be reduced. It will remain the same if we try to get a sharp image of remote houses, distant mountains, clouds or even the sun on paper. In other words, this distance is the shortest of all, in which it is possible to get a sharp image of objects.
For lenses with different optical power, this distance will be different, but for each lens it is constant, which allows it to be used as the main optical characteristic of a given lens. Therefore, it is called the main one. This also applies to any photographic lens. Regardless of the number of lenses it consists of, each photo lens is a collecting optical system, i.e., it acts like a single lens. Therefore, the lens is primarily characterized by the magnitude of its main focal length. This distance is indicated by the letter F or F and is expressed in centimeters (sometimes in millimeters). So, the designation “F = 5 cm” shows that the main focal length of this lens is 5 cm. For simplification, the main focal length is usually simply called the focal length.
What is the practical value of the lens focal length? First of all, the scale of the resulting image depends on it. It is directly proportional to the lens focal length. Compare the two pictures shown in Fig. 8. Both of them were made with the same device from the same distance, but in the first case, the lens focal length was half the length of the lens than in the second.
As you can see, the linear scale of the image in the first picture turned out to be half that. This phenomenon is based on the use in the same cameras of the so-called interchangeable lenses with different focal lengths, which allows you to take pictures on different scales, i.e. from the same point. Later we will get acquainted with such lenses in more detail.
Each camera is available with only one lens, but cameras of different formats have different focal lengths. For “Smena” cameras, lenses have a focal length of 4 cm, other small-format cameras have 5 cm. The camera has an “Amateur” and almost all other cameras in the 6 x 6 cm format The lenses have a focal length of 7.5-8 cm, and 6 x 9 cm cameras are equipped with lenses with a focal length of 10.5 cm.
As you can see, there is a connection between the camera format and the focal length of the lens: the more the format of the camera, the larger the focal length of the lens installed on it. It can also be found that the connection is natural and that the lens focal length is usually equal to or close to the diagonal of the frame for which the lens is intended. And in fact, the size of the 24 x 36 mm camera frame (low format) is 43.3 mm and the focal length of the lenses of such cameras is usually in the range from 4 to 5 cm. A 6 x 9 cm frame is 10.8 cm and the lenses of such cameras have almost the same focal length. How to explains it?
The area on which the lens gives the image is limited by the size of the frame, i.e., the format of the camera.
The photographic frame is always a rectangle or square, and the largest linear value in such geometric shapes is the diagonal. Knowing the diagonal of the frame and the magnitude of the focal length of the lens, you can use a simple graphic construction to determine one very important property of the lens: at what angle it covers the captured space. To do this, it is enough to draw a life-size rectangle on a piece of paper, as shown in Fig. 9, and draw a diagonal of this rectangle AB, lower the perpendicular to the middle of the diagonal and, laying on it the segment OC, equal to the focal length of the lens, connect the point C to the ends of the diagonal AB. The angle of the CA is the desired angle, called the angle of the image field.
Having done such a construction for lenses installed on cameras of different formats, you can see that the angle of the image field for all lenses is approximately the same and is in the range of 40-55 °. In the magnitude of this angle lies the secret of the pattern, which was mentioned above.
Experience has shown that the most convenient for the vast majority of photography are lenses, the angle of the image field of which is within the above limits. The difference between the values of the focal lengths of lenses of different cameras in format is explained by nothing more than the desire of designers to keep the same most convenient image field angle for all cameras. Lenses with this angle of the image field are called normal. They are often called universal. It is with lenses such as the main ones that are released in light.
One of the novice amateur photographers tried to assure the other that the larger the format of the camera, the more space they can cover when shooting. I want to warn you against such delusion. All cameras with normal lenses cover almost the same space. Two pictures shown in Fig. 10, this is convincingly confirmed. One of them was made with a 24 x 36 mm camera, the other from the same point with a 6 x 9 cm camera. Although the size of the images and the scale of the image on them are different, the boundaries of the photographed space they have are the same.
The no less important technical characteristic of the lens - its aperture - also depends on the focal length. As you can see, very important lens properties are associated with the focal length. It is no coincidence that its size is always indicated on the lens frame. But when choosing a camera, the least of all should be guided by the magnitude of the focal length of its lens. You already know that the focal length of the main lens is best matched to the frame format and matched to the most convenient image field angle. Choosing a device (camera) according to the lens focal length would be a useless exercise, but knowing this distance and its practical value is important.
What is the aperture?
Everyone who is going to buy a camera, the first thing to do is inquire about the aperture of its lens. Aperture is perhaps the most important technical characteristic of the lens. This is the measure of his light possibilities. The more aperture, the shorter the shutter speed can be when shooting. High aperture facilitates shooting fast moving objects and sports moments that require short shutter speeds. It expands the possibilities of shooting in dimly lit rooms, in twilight, in theaters, in sports halls, at night, from movie screens and TVs.
At first glance, it seems that the aperture depends only on the size of the lens, more precisely, on the diameter of its lenses. It is clear that the larger the lens diameter, the more light it transmits. However, it would be a mistake to think that this is the only thing. in Fig. 11 shows two lenses: "Industar-24" and "Industar-22". Which one has a large aperture? An inexperienced person would probably answer that the one that is bigger. And although this seems obvious, the aperture of these two lenses is exactly the same. This is explained by the fact that the aperture of the lens depends not only on the diameter of its lenses, but also on the magnitude of the focal length.
On the frames of the lenses of the aperture, it is denoted very conditionally, in the form of a ratio of two numbers, of which the first is always one. For example: 1:2 or 1:3.5, etc. The meaning of this designation is as follows: the diameter of the acting hole of the lens is taken as a unit, i.e., the hole that transmits light. Usually the size of this hole is equal to or very close to the magnitude of the front lens of the lens. The right side of the ratio shows how many times the diameter of this hole is less than the focal length of the lens. In general, the designation expresses the so-called relative hole of the lens.
A visual representation of the relative hole is given by Fig. 12. In its left part, it is shown what a relative hole in the Industar-22 lens with a focal length of 5 cm installed on the Zorkiy camera. As can be seen from the figure, the diameter of the acting hole of this lens is three and a half times smaller than its focal length. Its relative opening is 1:3.5. On the right side of the figure, the same scheme is given for the lens mounted on the amateur-2 camera, the focal length of which is four and a half times the diameter of its active opening. Its relative opening is 1:4.5.
Returning now to the previous figure, it is easy to understand why, despite the different size of the two lenses shown on it, the aperture of these lenses is the same: they have the same relative holes. the value of the relative hole can be expressed in the form of a fraction, i.e., instead of 1:3.5, write 1/3.5, and then it will become clear that the smaller the denominator of the fraction, the more relative the hole, and therefore the lens aperture is greater, since more the size of the fraction itself.
Now let's try to compare how many times the aperture of the lens with a relative hole of 1:2 more than that of a lens with a relative hole of 1:4. At first glance, it may seem that for this it is necessary to divide the larger of these quantities into smaller ones, i.e. 1/2: 1/4. However, such a decision is grossly erroneous. In this case, the answer will be equal to two, meanwhile, the aperture of the first of the lenses is greater than the second, not two, but four times. What explains this? Let's remember something from an elementary course in geometry and physics, and everything will become clear.
The amount of light passing through the lens depends on the area of the lens of the acting hole. The latter has the shape of a circle, and the area of circles, as is known from geometry, refers as squares of their diameters. Consequently, the amount of light passing through the lens is proportional to the square of the diameter of its active hole. Thus, if the diameter of the acting hole of one lens is twice as large as the other, then with the same focal length of both lenses, the first is greater than the second, not 2 times, but 2^2, i.e., 4 times.
Now let's see what is the dependence of the aperture on the magnitude of the focal length. From the course of physics it is known that the surface illumination is inversely proportional to the square of the distance from the light source to the illuminated surface. The source of light in the camera is the lens, the surface is illuminated by the film, and the distance is the focal length of the lens. Hence, if the focal length of one lens is twice as large as the other, then with the same diameter of the acting holes of both lenses of the first aperture is less than the second, not 2 times, but 22 times, i.e., 4 times. Summing up all of the above, the aperture of the lens can be expressed as follows:
F=Lense opening diameter / Focal length
Thus, the relative opening characterizes the aperture of the lens, but does not express it numerically. In everyday life, these concepts are very often confused, calling the relative hole a luminosity, but a competent photographer will never say that. Interested in the aperture of the lens, he will ask: what is its relative hole? At the modern level of development of optical technology, photo lenses with a relative opening of 1:1 are considered superfast. Such lenses are very rare. 1:2 - 1:1.5 relative hole lenses are considered very fast. Enough lenses with a relative hole of the order of 1: 3.5 - 1:2.8. The aperture of lenses with a relative hole of 1:4.5 - 1:4 is currently considered average, and with a relative hole of 1:5.6 or less - a small one.
However, the value of the aperture should not be overestimated too much. The ability to photograph with short exposures under adverse light conditions depends not only on the aperture; No less depends on the photosensitivity of the photographic material, and the light sensitivity of modern photographic films is so high that in most cases it is possible to shoot with short shutter speeds with a not very large lens aperture. And in no case should you think that the more aperture of the lens, the higher the sharpness of the image it gives. The sharpness of the image does not depend on the aperture. It depends mainly on the design of the lens and the accuracy of its manufacture.
Thus, the aperture of the lens is not as important as it might seem at first glance, and the desire to purchase a camera with a very fast lens at all costs is not always justified.
Focal lengt (Main focal Lengt)
If you direct a beam of light rays parallel to the main optical axis of the lens onto a converging (for example, biconvex) lens, as shown in Fig. 7, in the upper left corner, then after refraction in the lens these rays will converge at the main focus. The distance from the lens to the main focus is the main focal length of the lens.
To a reasonable approximation, it can be determined by placing a lens or objective in the path of the sun's rays, which are practically parallel, and obtaining a sharp image of the sun on paper. The distance between the lens and the paper will be the main focal length of the lens. It can be measured with a ruler.
Why is this distance called the main one?
Using a lens, you can notice that as the distance between the object and the lens changes, the distance from the lens to the image of the object also changes.
Let's do the following experiment. Let us take a biconvex lens and a sheet of white paper and, placing the lens at a short distance from a burning lamp, we will obtain a sharp image of the lamp on the paper. After measuring the distance between the lens and the paper, we will begin to move further away from the lamp, maintaining the sharpness of the image. It is easy to see that the distance between the lens and paper will first decrease rather quickly, and then more slowly, as if fading, and finally the moment will come when it will stop shortening. And no matter how far we move from the lamp, the distance from the lens to the paper will practically not be reduced. It will remain the same if we try to get a sharp image of remote houses, distant mountains, clouds or even the sun on paper. In other words, this distance is the shortest of all, in which it is possible to get a sharp image of objects.
For lenses with different optical power, this distance will be different, but for each lens it is constant, which allows it to be used as the main optical characteristic of a given lens. Therefore, it is called the main one. This also applies to any photographic lens. Regardless of the number of lenses it consists of, each photo lens is a collecting optical system, i.e., it acts like a single lens. Therefore, the lens is primarily characterized by the magnitude of its main focal length. This distance is indicated by the letter F or F and is expressed in centimeters (sometimes in millimeters). So, the designation “F = 5 cm” shows that the main focal length of this lens is 5 cm. For simplification, the main focal length is usually simply called the focal length.
What is the practical value of the lens focal length? First of all, the scale of the resulting image depends on it. It is directly proportional to the lens focal length. Compare the two pictures shown in Fig. 8. Both of them were made with the same device from the same distance, but in the first case, the lens focal length was half the length of the lens than in the second.
As you can see, the linear scale of the image in the first picture turned out to be half that. This phenomenon is based on the use in the same cameras of the so-called interchangeable lenses with different focal lengths, which allows you to take pictures on different scales, i.e. from the same point. Later we will get acquainted with such lenses in more detail.
Each camera is available with only one lens, but cameras of different formats have different focal lengths. For “Smena” cameras, lenses have a focal length of 4 cm, other small-format cameras have 5 cm. The camera has an “Amateur” and almost all other cameras in the 6 x 6 cm format The lenses have a focal length of 7.5-8 cm, and 6 x 9 cm cameras are equipped with lenses with a focal length of 10.5 cm.
As you can see, there is a connection between the camera format and the focal length of the lens: the more the format of the camera, the larger the focal length of the lens installed on it. It can also be found that the connection is natural and that the lens focal length is usually equal to or close to the diagonal of the frame for which the lens is intended. And in fact, the size of the 24 x 36 mm camera frame (low format) is 43.3 mm and the focal length of the lenses of such cameras is usually in the range from 4 to 5 cm. A 6 x 9 cm frame is 10.8 cm and the lenses of such cameras have almost the same focal length. How to explains it?
The area on which the lens gives the image is limited by the size of the frame, i.e., the format of the camera.
The photographic frame is always a rectangle or square, and the largest linear value in such geometric shapes is the diagonal. Knowing the diagonal of the frame and the magnitude of the focal length of the lens, you can use a simple graphic construction to determine one very important property of the lens: at what angle it covers the captured space. To do this, it is enough to draw a life-size rectangle on a piece of paper, as shown in Fig. 9, and draw a diagonal of this rectangle AB, lower the perpendicular to the middle of the diagonal and, laying on it the segment OC, equal to the focal length of the lens, connect the point C to the ends of the diagonal AB. The angle of the CA is the desired angle, called the angle of the image field.
Having done such a construction for lenses installed on cameras of different formats, you can see that the angle of the image field for all lenses is approximately the same and is in the range of 40-55 °. In the magnitude of this angle lies the secret of the pattern, which was mentioned above.
Experience has shown that the most convenient for the vast majority of photography are lenses, the angle of the image field of which is within the above limits. The difference between the values of the focal lengths of lenses of different cameras in format is explained by nothing more than the desire of designers to keep the same most convenient image field angle for all cameras. Lenses with this angle of the image field are called normal. They are often called universal. It is with lenses such as the main ones that are released in light.
One of the novice amateur photographers tried to assure the other that the larger the format of the camera, the more space they can cover when shooting. I want to warn you against such delusion. All cameras with normal lenses cover almost the same space. Two pictures shown in Fig. 10, this is convincingly confirmed. One of them was made with a 24 x 36 mm camera, the other from the same point with a 6 x 9 cm camera. Although the size of the images and the scale of the image on them are different, the boundaries of the photographed space they have are the same.
The no less important technical characteristic of the lens - its aperture - also depends on the focal length. As you can see, very important lens properties are associated with the focal length. It is no coincidence that its size is always indicated on the lens frame. But when choosing a camera, the least of all should be guided by the magnitude of the focal length of its lens. You already know that the focal length of the main lens is best matched to the frame format and matched to the most convenient image field angle. Choosing a device (camera) according to the lens focal length would be a useless exercise, but knowing this distance and its practical value is important.
What is the aperture?
Everyone who is going to buy a camera, the first thing to do is inquire about the aperture of its lens. Aperture is perhaps the most important technical characteristic of the lens. This is the measure of his light possibilities. The more aperture, the shorter the shutter speed can be when shooting. High aperture facilitates shooting fast moving objects and sports moments that require short shutter speeds. It expands the possibilities of shooting in dimly lit rooms, in twilight, in theaters, in sports halls, at night, from movie screens and TVs.
At first glance, it seems that the aperture depends only on the size of the lens, more precisely, on the diameter of its lenses. It is clear that the larger the lens diameter, the more light it transmits. However, it would be a mistake to think that this is the only thing. in Fig. 11 shows two lenses: "Industar-24" and "Industar-22". Which one has a large aperture? An inexperienced person would probably answer that the one that is bigger. And although this seems obvious, the aperture of these two lenses is exactly the same. This is explained by the fact that the aperture of the lens depends not only on the diameter of its lenses, but also on the magnitude of the focal length.
On the frames of the lenses of the aperture, it is denoted very conditionally, in the form of a ratio of two numbers, of which the first is always one. For example: 1:2 or 1:3.5, etc. The meaning of this designation is as follows: the diameter of the acting hole of the lens is taken as a unit, i.e., the hole that transmits light. Usually the size of this hole is equal to or very close to the magnitude of the front lens of the lens. The right side of the ratio shows how many times the diameter of this hole is less than the focal length of the lens. In general, the designation expresses the so-called relative hole of the lens.
A visual representation of the relative hole is given by Fig. 12. In its left part, it is shown what a relative hole in the Industar-22 lens with a focal length of 5 cm installed on the Zorkiy camera. As can be seen from the figure, the diameter of the acting hole of this lens is three and a half times smaller than its focal length. Its relative opening is 1:3.5. On the right side of the figure, the same scheme is given for the lens mounted on the amateur-2 camera, the focal length of which is four and a half times the diameter of its active opening. Its relative opening is 1:4.5.
Returning now to the previous figure, it is easy to understand why, despite the different size of the two lenses shown on it, the aperture of these lenses is the same: they have the same relative holes. the value of the relative hole can be expressed in the form of a fraction, i.e., instead of 1:3.5, write 1/3.5, and then it will become clear that the smaller the denominator of the fraction, the more relative the hole, and therefore the lens aperture is greater, since more the size of the fraction itself.
Now let's try to compare how many times the aperture of the lens with a relative hole of 1:2 more than that of a lens with a relative hole of 1:4. At first glance, it may seem that for this it is necessary to divide the larger of these quantities into smaller ones, i.e. 1/2: 1/4. However, such a decision is grossly erroneous. In this case, the answer will be equal to two, meanwhile, the aperture of the first of the lenses is greater than the second, not two, but four times. What explains this? Let's remember something from an elementary course in geometry and physics, and everything will become clear.
The amount of light passing through the lens depends on the area of the lens of the acting hole. The latter has the shape of a circle, and the area of circles, as is known from geometry, refers as squares of their diameters. Consequently, the amount of light passing through the lens is proportional to the square of the diameter of its active hole. Thus, if the diameter of the acting hole of one lens is twice as large as the other, then with the same focal length of both lenses, the first is greater than the second, not 2 times, but 2^2, i.e., 4 times.
Now let's see what is the dependence of the aperture on the magnitude of the focal length. From the course of physics it is known that the surface illumination is inversely proportional to the square of the distance from the light source to the illuminated surface. The source of light in the camera is the lens, the surface is illuminated by the film, and the distance is the focal length of the lens. Hence, if the focal length of one lens is twice as large as the other, then with the same diameter of the acting holes of both lenses of the first aperture is less than the second, not 2 times, but 22 times, i.e., 4 times. Summing up all of the above, the aperture of the lens can be expressed as follows:
F=Lense opening diameter / Focal length
Thus, the relative opening characterizes the aperture of the lens, but does not express it numerically. In everyday life, these concepts are very often confused, calling the relative hole a luminosity, but a competent photographer will never say that. Interested in the aperture of the lens, he will ask: what is its relative hole? At the modern level of development of optical technology, photo lenses with a relative opening of 1:1 are considered superfast. Such lenses are very rare. 1:2 - 1:1.5 relative hole lenses are considered very fast. Enough lenses with a relative hole of the order of 1: 3.5 - 1:2.8. The aperture of lenses with a relative hole of 1:4.5 - 1:4 is currently considered average, and with a relative hole of 1:5.6 or less - a small one.
However, the value of the aperture should not be overestimated too much. The ability to photograph with short exposures under adverse light conditions depends not only on the aperture; No less depends on the photosensitivity of the photographic material, and the light sensitivity of modern photographic films is so high that in most cases it is possible to shoot with short shutter speeds with a not very large lens aperture. And in no case should you think that the more aperture of the lens, the higher the sharpness of the image it gives. The sharpness of the image does not depend on the aperture. It depends mainly on the design of the lens and the accuracy of its manufacture.
Thus, the aperture of the lens is not as important as it might seem at first glance, and the desire to purchase a camera with a very fast lens at all costs is not always justified.
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