Lens - essential element any camera. And focal length is the most important characteristic of a lens. However, novice amateur photographers experience complete confusion with this characteristic. They cannot understand: for example, a lens with a focal length of 24-70 mm on a full-matrix camera is it good or bad? Is 15-44 mm on a “cropped” DSLR normal or not enough? Is 7.1-28.4 mm on a point-and-shoot camera quite small or is it still ok? Well, let's figure out what the focal length of a lens is and what its different values ​​mean. A lens is a system consisting of several lenses. The image of the object being photographed enters the lens, is refracted there and reduced to one point at a certain distance from the back of the lens. This point is called focus(focus point), and the distance from the focus to the lens (lens system) is called focal length.

Now let’s talk about what these or other focal lengths mean in practical terms. Initially, let’s agree that we are now talking about a lens designed for shooting on a full-matrix camera (in this article we talked about what a “full matrix” is). Let's take a purely practical look at the differences between frames taken with one focal length or another. We shoot from one point and change focal lengths from 24 to 200 mm. Focal length 24 mm.
Focal length 35 mm.
Focal length 50 mm.
Focal length 70 mm.
Focal length 100 mm.
Focal length 135 mm.
Focal length 200 mm.
Obviously, the shorter the focal length, the more is placed in the frame, and the longer the focal length, the closer the lens brings distant objects. Short focal lengths are used for shooting all kinds of images: landscapes, architecture, large groups people. Long focal lengths are used for shooting, for example, animals and birds, for sports photography when you need to catch close up some spectacular shot. A focal length of 50 mm approximately corresponds to the viewing angle of the human eye (46°). Lenses with a focal length of less than 35mm are called wide-angle. With their help, it is convenient to photograph nature and architecture, however, it should be borne in mind that the wider the angle (smaller focal length), the greater the distortions caused by the laws of optics will be present in the photographs. For example, if you shoot high-rise buildings with a lens with a focal length of 24 mm, then closer to the edges of the frame on the right and left the buildings will appear tilted - here is an example.
Lenses with a focal length of less than 20mm are called ultra-wide-angle lenses, and they distort the image very much. (There is also a separate type of lens with a fisheye effect.) Here is an example photo (from here) taken with a wide-angle fisheye with a focal length of 8 mm.
Lenses with long focal lengths are called “long focal lengths”, and those with very long focal lengths are called “telephoto lenses”. In general, the classification there is approximately as follows: Lenses come with a fixed focal length (the so-called “primes”) and with a variable focal length (the so-called “zooms” from the word zoom, bring closer). As a rule, lenses with a fixed focal length take better pictures (and are cheaper) than zooms set to the same focal length. That is, for example, in general, a 24 mm wide-angle will provide better quality than a 24-70 mm zoom set to 24 mm. (There are exceptions, but we won’t get into those jungles now.) And now we come to a very important question. What is this strange range of focal lengths on my Fujifilm X20, you may ask? It says 7.1-28.4 mm. Is it like a super mega extra wide angle? No. The fact is that when we talk about cameras with a cropped matrix, the physical focal length of the lens does not change (it cannot change), however, since much less fits into the frame on a cropped matrix, it turns out that the “angle of view” of the lens narrows, and Accordingly, for a given matrix the focal length will be different. Precisely “as if different”, because if the lens has a focal length of 50 mm, physically it will remain that way on any matrices. But the shots will be different. I'll explain now. Let's say we have a lens with a focal length of 50 mm. It forms a circular image, which, superimposed on the full-size matrix, gives us a full frame - there it is, marked in the illustration.
We put the same lens on a camera with a cropped matrix - for example, with a crop factor of 2. What will a frame taken with the same lens look like? It will appear within the blue rectangle in the illustration. That is, less. And less means the object will be closer, so it turns out that when shooting with a lens with a focal length of 50 mm on a camera with a crop factor 2 matrix, the focal length will be equivalent to shooting with a lens of 100 mm (50 mm times the crop factor) on the camera with a full-size matrix. The problem is that cropped camera lenses usually indicate the physical focal length of the lens. And in order to understand what these numbers generally mean, you need to multiply the specified focal length by the size of the crop - then you will get the numbers of the focal length (distances for zoom) in the equivalent of a full-matrix camera (35mm matrix) and you will understand what range of focal lengths is present in this camera Example. Fujifilm Finepix X20 camera, zoom range - 7.1-28.4 mm. The crop factor of this camera's matrix is ​​3.93. So we multiply 7.1 by 3.93 and 28.4 by 3.93 - we get a range (rounded) of 28-112 mm in 35 mm equivalent. In general, the most common range for a digital camera. Second example. Amateur DSLR with a kit lens. The lens has a range of 18-55mm. The crop factor of the matrix is ​​1.6. Multiply - we get 29-88 mm. The range is very so-so, but you can use it. Thus, in order to clearly understand what focal lengths are available in your camera (or in the camera you are going to buy), you need to multiply the focal range numbers indicated on the lens by the crop factor - this will give you data on focal lengths of 35- mm equivalent, which will be quite clear to you. It is clear that for full-format cameras with their “native” lenses, no recalculations need to be made. By the way, sometimes, for the convenience of users, manufacturers write on non-replaceable camera lenses their physical focal length, and its equivalent for 35 mm - like, for example, the Sony RX10 camera, where the physical range is 8.8-73.3, and on the installed The 2.7 crop produces an excellent range of 24-200 mm: from a good wide-angle to a very decent telephoto lens.

Knowing what focal length is and what the features are is especially important when purchasing lenses. This tutorial will give you information about how different focal length lenses work, how to use them creatively, and choose the ones that are right for you.

Step 1 - What does this actually mean?

The focal length of your lens mainly determines what zoom your photos will be at: what larger number, the greater the effect of zooming in and out.

Focal length is often misunderstood as being measured from the front or rear lens. In reality it is the distance from the point of convergence to the sensor or film in the camera. Look at the diagram below where this is explained.

Step 2 - Different focal lengths and how they are used

Ultra wide angle 12-24mm

These lenses are considered highly specialized and are not often included in the average photographer's lens kit. They create such a wide viewing angle that the image may appear distorted because our eyes are not used to this kind of range. They are often used in event and architectural photography, for shooting in confined spaces. Wide-angle lenses seem to place the photographer in the center of events, making him no longer an observer, but a participant, creating the effect of presence. They are not very suitable for portrait photography, as they increase the perspective so much that facial features can be distorted and look unnatural.

Wide-angle 24-35 mm

Here you will find many kit lenses for full frame cameras, they start at a focal length of 24mm, where the angle is wide but the distortion is not yet as pronounced. These lenses are widely used for reportage photography, and by photojournalists for documentary photography, because they have a wide enough angle to include a large number of objects, and at the same time, distortion is not so significant.

Standard 35-70 mm

It is in this focal length range of 45-50 mm that the angle of view of the lens will approximately correspond to how our eyes see (excluding peripheral vision). I personally would like to use this range when shooting on the street or when meeting friends in the pub or dining table. A standard lens such as the 50mm f/1.8 is great inexpensive and gives excellent results. A fixed focal length lens will always give best quality images than zoom. This is because it is built for a single purpose. He does one job well and several jobs poorly.

Initial telephoto 70-105 mm

This range is usually at the extreme end for kit lenses. This is where telephoto lenses and prime lenses for portrait photography begin (about 85 mm). This good choice for portrait photography, as it can take close-up portraits without distortion, and also achieve separation of the subject from the background.

Tele 105-300 mm

Lenses in this range are often used for distant scenes such as buildings, mountains. They are not suitable for landscapes as they compress the perspective. Longer focal length lenses are primarily used for sports or wildlife photography.

Step 3 - How does focal length affect perspective?

I already talked about this in the previous section, but to give you a better idea of ​​the effect of focal length on perspective, I took 4 photos of the same objects at different focal lengths and compared them. Three objects (cans of soup) were in the same position at a distance of 10 cm from each other in each photograph. It is worth noting that the pictures were taken with a crop camera, so the focal length will be slightly longer.

Now let's talk about what the crop factor is. Essentially this means that if you put any full frame lens (EF, FX, etc.) on a body with a crop factor, part of the image will be cut off. The trim factor will be approximately 1.6. In real terms, this means that if you shoot with a 35mm lens, you will get the same result as if you shot with a 50mm lens.

How this works is shown in the pictures below. This is actually a zoomed image, narrowing the angle of view of the lens.

Even on lenses designed for cropped cameras (EF-S, DX), a similar effect will be observed, since focal lengths are always indicated for the full frame. It’s just that these lenses at full frame will give a strong vignetting effect, since the image is not projected over the entire area of ​​the frame.

That's it! And two more completely different photographs taken at different focal lengths. The first is at 24 mm, the second is at 300 mm (both on a camera with a crop sensor).

And at the same time, I would recommend the community - it is aimed at beginners in photography who want it, i.e. photography, master) We do homework together, discuss, criticize, write lessons and educational programs)
Read the rules and join!

In this lesson we will learn how to decipher lens markings and talk in detail about what focal length is and how it affects the image.

*1. Lens specifications*
So, let's take a look at our lenses, or rather at the markings written on their rim.
What interesting things can we see there, besides the name of the manufacturer? Here are some interesting numbers:
17-55 f/2.8
55-300 f/4.5-5.6
50mm f/1.4

So the first numbers are focal length(FR). Lenses come with variable and constant PR.
In the examples above, "17-55" and "55-300" are zoom lenses. This means that the FR of the first lens can change from 17mm (at the “short” end) to 55mm (at the “long” end). In common parlance, changing the focal length of a lens is called zoom.

A 50mm lens is a prime lens. This means that this lens does not have a “zoom” and if you want to change the framing of the photo, move closer or further from the subject, you will have to do it with your own feet :)
It is believed that lenses with constant phase response give a better picture, this is due to the fact that adding a zoom “opportunity” complicates the design of the lens. Consequently, either the price of such a lens increases, or the quality decreases slightly. But, naturally, this is not an ironclad rule, and the difference in quality can often only be noticed by a trained eye, and even then at 100% crop.

The following numbers on the lens, which usually go through f/, indicate the maximum f-number, which can be set on the lens.
In the examples above, f/2.8 means that the maximum aperture can be opened to a value of 2.8, while the maximum aperture opening does not depend on the focal length.
For example, on a 55-300 f/4.5-5.6 lens, the opening of the aperture depends on the focal length. Those. at a focal length of 55mm, the aperture opens to f/4.5, and when the zoom is increased to 300mm, the aperture can only be opened to f/5.6.

*2. Focal length*
Let's now see what focal length is and what it affects.

*2.1 Frame*
Naturally, the most obvious use of focal length is cropping.

At low FR values, a large area falls into the frame, and the viewing angle is very wide. Therefore, lenses with a short focal length are called wide angle(“widths”), 18-24mm. These lenses are typically used for landscape photography.

Lenses with a very short focal length (10-12mm) are called fish eye, their viewing angle can reach almost 180 degrees, but the pictures turn out almost caricatured, with insane perspective distortions.

The longer the focal length, the smaller the viewing angle of the lens, the less space gets into the frame. At the same time, the image “gets closer”. Lenses with very long focal lengths are called telephoto lenses(200-300mm and more), such lenses are used for shooting wildlife, athletes on the football field, i.e. in cases where you can’t get close to the subject of photography.

Lenses with an AF of 35-50mm are usually classified as universal lenses, so-called staff members, i.e. Suitable for shooting a variety of scenes. Such lenses are called standard lenses because they are most often worn without removing them from the camera, for all occasions. Naturally, each person can have his own staff, depending on his preferences.

Lenses with focal lengths of 50-125mm are best suited for shooting portraits, and they can roughly be classified as "portrait painters", since they give the least perspective distortion.

For more visual illustration I will give 2 pictures of what has been said. Both pictures were taken from the same shooting point. But on the first focal length = 18mm, and on the second - 70mm. As you can see, at 18mm almost the entire room was included in the frame, but at 70mm the image was “closer” and only the person fit into the frame.

(note: the pictures have little artistic value and were taken solely for the purpose of illustrating differences in focal lengths)

*2.2 Perspective distortion*
Perspective distortion is a distortion of the proportions of the subject being photographed.
These distortions appear when the camera is very close to the subject being photographed.
Thus, the further we move away from the subject, the less perspective distortion we get.

Now let's see what focal length has to do with it.
Let's say we need to take a facial portrait of a person. If we use a small focal length, then in order to get only the face into the frame, without the surrounding environment, we will have to get very close to the subject, which will cause terrible perspective distortions. We will get not a portrait, but a caricature.
The more we increase the focal length, the further we will need to move away from the subject, and accordingly, the less perspective distortion will be.

It is believed that when shooting portraits, it is best to use lenses with a focal length of at least 50mm. (However, in photographic circles there is a constant debate on the topic “Fifty dollars is not a portrait!” And indeed, a front portrait at 50mm will have slight perspective distortions. But, for example, a half-length portrait will be quite good)
In general, a classic portrait lens is an 85mm fast lens :)

Again, a few photos as an example.
1 photo - 18mm - a completely caricatured image, the person being portrayed will rarely like this result :)
2 photos - 35mm - better, but distortion is still noticeable;
3 photos - 70mm - and very close to the truth.

*2.3 Exposure and focal length*
The higher the focal length, the shorter the shutter speed needs to be set to avoid “shake” (blurring of the frame due to shaking hands). Do you think your hands aren't shaking? Try putting a 300mm lens on your camera and looking through the viewfinder, you will be surprised :)

For approximate determination required endurance you can use the formula -
[shutter speed] = [unit] divided by [focal length].
Those. with a focal length of 18mm, a shutter speed of 1/18 is sufficient, and with a focal length of 200mm, the shutter speed should be reduced to 1/200.

*2.4 Crop factor*
When talking about focal length, one cannot fail to mention the “crop factor”.
The reference matrix size is considered to be the size of a standard 35mm film frame.
Digital cameras with a matrix the size of a 35mm film frame are called “full frame”. Cameras with a matrix size smaller than 35mm film are cropped.

At the same time, the lenses will give a slightly different picture on a cropped and full-format matrix: the focal length of the lens will “increase” in proportion to the crop factor of the matrix.
Those. If we have a 50mm lens, then using it on a camera with a crop factor of 1.5, we will get an image similar to that obtained when shooting with a 75mm lens on a “full frame” camera.

*3. Diaphragm*
When shooting a portrait, we all want to get a three-dimensional, vibrant image.
First of all, of course, this is achieved by a light-shadow pattern. But don’t forget about depth of field - a correctly selected depth of field allows you to separate the portrait from the background, making the photo multifaceted and deep.

As we all remember, it is the aperture that allows you to adjust the depth of field. Opening the aperture to its maximum will allow you to leave only your eyes in focus, leaving the rest of the image in a beautiful watercolor bokeh.

I admit, I love the most blurry portraits. and not only portraits, to be honest, I’m just a fan of blur :) But, of course, such extreme solutions are not at all necessary, you can close the aperture so much that the entire subject is clear, but a beautiful bokeh in the background will always decorate a portrait) The main thing is to watch out so that the eyes are in focus, this is the center of any portrait

*4. Exercise*
The tasks were written for community members, but what if any of you also want to complete them for fun?) Let us know the results in the comments)

1. Study the lenses you have, find the lens with the smallest DF. Using a wide-angle lens, shoot an “interior portrait” or “landscape portrait”; in the photo, try to convey the ratio of scales, volume and spaciousness of the space surrounding the subject.

2. Shoot a portrait using the longest focal length on your lens and the widest aperture. Vary the opening of the aperture to achieve the degree of blur that suits you best. Remember that the eyes must be in focus)

3. And I suggest you have a little fun :) Take a portrait, setting the smallest focal length, getting as close as possible to the subject (by the way, a “hand-held” self-portrait is just from the same opera). Achieve maximum perspective distortion and caricature look :)

It is often mistakenly believed that focal length- this is the distance to the focusing object. This is, of course, not true. Focal length- one of the most important characteristics lens, which determines its viewing angle, that is, the sector of space that falls into the frame. The shorter the focal length, the larger the viewing angle of the lens.

Depending on the viewing angle, lenses are divided into wide-angle, normal and telephoto lenses.

Wide angle A lens is considered to have an angle of view greater than that of the human eye. The focal length of wide-angle lenses is 35 millimeters or less.

The image obtained by such a lens has a rather pronounced perspective and background objects seem smaller than we are used to seeing them, but the viewing angle of such a lens allows you to shoot in tight spaces without any problems. Here are examples of photos taken with a 16mm ultra-wide-angle lens.

We see how high angle This lens has a wide range of views, but it comes at the cost of significant perspective distortions - they are especially noticeable in the corners of the image. Here's another photo taken with a 16mm lens:

The same thing - the huge angle of view made it possible to fit a huge amphitheater into the frame. A pronounced perspective effect is also noticeable - small objects in the foreground seem huge, and large objects in the background seem unusually small.

Wide Angle Lenses are used in cases where one frame needs to cover a large space - mainly in landscape and interior photography. For a large angle of view you have to pay with a specific “aggressive” perspective - the lens distorts the proportions of objects in the foreground and background (see photo with the amphitheater), and also has a tendency to collapse vertical lines (see photo indoors).

Normal A lens whose angle of view is close to that of the human eye is considered. Another, more correct definition of a normal lens is a lens that has a focal length equal to the diagonal of the frame (in the case of a film frame, 43 mm). The focal length of normal lenses may vary slightly and ranges from 40 to 50 mm. Compared to a wide-angle lens, the angle of view of a normal lens may seem small, but the lens has a calmer perspective. Photos taken with such a lens are perceived most naturally, sometimes called the “effect of presence.” Here is an example photo taken with a 50mm lens.

Please note that the perspective of a normal lens is much more familiar and “calmer” than that of a wide-angle lens. The ratio of the sizes of objects in the foreground and background is familiar to the eye - this is the main advantage of a normal lens. Reverse side medals - in order to photograph a sufficiently large object, you need to move far enough away from it. This is not very convenient and not always possible. A normal lens is best suited for shooting in open spaces, so-called “street photography”. For landscape and indoor photography, this lens may not have enough field of view to fit everything you need into the frame.

Telephoto lenses have a focal length of 60 mm or more. It’s easy to guess that the longer the focal length, the stronger the lens “zooms in”. Telephoto lenses with focal lengths up to 135 mm are often called "portrait lenses". They provide a relatively small zoom effect, so they won’t be able to take close-up shots of distant objects, but the perspective of these lenses is optimal for portrait photography—distortion of facial proportions is minimal. Here are two examples: the first portrait was taken with a wide angle (28 mm):

The photograph shows that the proportions of the face are seriously distorted - it looks excessively convex and even the eyes seem to be looking in different directions. Conclusion - if you shoot a portrait with a wide angle, it will look more like a cartoon!

Another example is a photograph taken with a focal length of 80mm:

Now the proportions are all right! Plus, the increased focal length made it possible to “stretch” and blur the background, now it does not distract us from the main objects.

When shooting even closer-up portraits, when the face occupies most of the frame, lenses with an even larger focal length are used - up to 135 mm. A longer focal length is rarely used in a classic portrait, since due to the weak perspective the face may look too flat. On the other hand, it can smooth out some imperfections, such as a too long nose.

Long focal length lenses are used when it is not possible to get close to the subject.

Please note that the photograph does not convey the depth of the landscape well - the objects in the foreground are approximately the same size as those in the background. Because of this, the landscape does not look natural. Telephoto lenses are also used when photographing shy birds and animals, for shooting sports photo reports, when you have to shoot from the stands, and the distance to the subject can be several tens of meters.

So we decided which scenes are best to shoot at which focal lengths. For simplicity, we summarize this information in a small table.

Of course, the ranges of focal lengths are approximate - it is impossible to provide for all genres and all the author's ideas in a small tablet! In real situations, the optimal focal length may differ significantly from what is given in the table.

How to find out the focal length of a lens?

To find out the focal length of a lens, just read its markings. Let's take a common Canon lens - the “whale” one (in the picture on the left)...

The arrow in the figure marks the inscription indicating the range of focal lengths - from 18 to 55 millimeters. Similar inscriptions are on all lenses without exception. If there is only one number, then the lens has a fixed focal length and does not have zoom.

Another important point, which cannot be ignored - this is the so-called equivalent focal length. Those focal lengths discussed in the section on viewing angle and perspective apply to film cameras, as well as digital ones, which have a matrix the size of a film frame - 36 * 24 mm. Such matrices are called “full frame” or FF (from English Full Frame - full frame). They are “inserted” mainly into professional cameras. In most amateur and semi-professional devices, the matrix size is 1.5-1.6 times smaller than the film frame. Matrices of this size are called APS-C (Advanced Photo System - Classic). What happens if, say, a lens with a focal length of 50 mm is attached, for example, to a Canon EOS 650D with an APS-C matrix? How will the picture differ from the full-frame Canon EOS 5D Mark II? Let's look at the pictures...

If the EOS 5D matrix receives the entire image formed by the lens, then only the central part of the image falls on the amateur 650D matrix; it is marked with a yellow dotted frame.

As a result, photographs taken by different devices with the same lens will differ slightly from each other.

It is easy to notice that on an APS-C matrix, a 50 mm lens seems to give a smaller viewing angle. Therefore, to get the same viewing angle as a full frame, you need to reduce the focal length. How much should it be reduced to get the same picture as the full frame? Right! The same amount as the APS-C matrix is ​​smaller than the FF matrix, that is, 1.6 times! By the way, the coefficient 1.6 is called crop factor. The higher the crop factor, the smaller the physical size of the matrix.

50mm: 1.6 = 31.25 mm

Thus, we calculated what focal length the lens should have in order to provide the same viewing angle on an APS-C matrix as that of a 50 mm lens at full frame - approximately 31 mm. In such cases they say: a lens with a real focal length of 31 mm on a 1.6 crop has an equivalent focal length of 50 mm.

Now let’s make an addition to the table with focal lengths that was drawn above...

Now let’s look at the distance scale of the kit lens and use imaginary multi-colored markers to mark the areas of application on it, something like this:

Naturally, the picture is approximate, but it clearly helps to determine what types of shooting a kit lens is suitable for. The 18-55 mm range was not chosen lightly - it allows you to perform the most popular types of amateur photography. Of course, the possibilities of a kit lens are not limitless. They are not recommended to take close-up portraits (the closest shot, the face in the entire frame); for this, a lens with a focal length of about 85 mm is desirable (so that the equivalent focal length is 135 mm). If you try to shoot such portraits at a focal length of 55 mm, you will have to do it from too close a distance, which will make the perspective distortions of the facial proportions noticeable (of course, not as much as at a wide angle, but it will still be noticeable). Also, it is impossible to shoot distant objects with a kit lens due to the lack of focal length.

People often ask me: if you buy a “superzoom” (for example, 18-200 mm), can you do beautiful portraits? Agree, it’s a tempting idea - to buy one lens for all occasions! Alas, everything is not so simple. On the one hand, the range of focal lengths of a “superzoom” really makes it universal, but on the other hand, due to its relatively small aperture ratio, it cannot always provide a shallow depth of field, which in most cases determines the beauty of a portrait. What depth of field is, why it is needed and how to control it will be discussed in the next chapter!

Nikon photography simulator with different focal lengths

See how the field of view of the lens changes with changing focal length and when used on a full frame sensor (FX) and on a 1.5 crop sensor (DX).

Questions for self-control

1. Determine the range of actual and equivalent focal lengths of your lens.
2. What types of shooting is your lens best suited for?
3. What types of shooting does your lens not support?

The camera is an optical system of lenses and one of its main characteristics is focal length. Actually, the focal length determines the scale of the image that you will see in the photographs - the larger the focal length of the lens, the visually closer the subject in the photograph will be.

The focal length of a lens is the distance from its optical center ( correct name - convergence point) to the camera matrix, that is, to the plane on which the image is projected.

Light rays reflecting from the object being photographed pass through the lens (lens), are refracted there and converged into optical center, after which they fall on the camera sensor. The plane passing through the optical center and perpendicular to the main optical axis of the lens is called focal plane. An image is formed on it, which in an “inverted” form is transferred to the sensor.

In fact, the whole principle of “transferring” a real image to a camera sensor can be represented like this:

At the same time, with increasing focal length, as the image is scaled and zoomed in, the angle of coverage visible by the lens will narrow. The figure shows why this happens.

Focal length is measured in millimeters and is usually marked on the lens barrel. There are lenses with fixed focal length. They indicate one value in millimeters - for example, 100mm.

If two values ​​are specified, for example 18 and 55 mm, then these are the minimum and maximum focal lengths that are available in this lens with variable focal length. Such lenses can change the focal length within these limits.

Typically, the longer the focal length of the lens, the longer it is...although there are exceptions.

Let's take a purely practical look at the differences between frames taken with one focal length or another. We shoot from one point and change focal lengths from 14 to 300 mm:

Additionally, focal length affects the perspective of the image. A long focal length makes the image appear flatter. Below is an example of what an image looks like taken with lenses of different focal lengths (for this example, the ruler was positioned at an angle of 45 degrees to the optical axis of the lens and the distance between the vases was 8 cm):