Lenses are transparent objects that can refract sunlight. They are mainly made from glass. The words "refract light" refers to the ability to change the direction of propagation of incident light rays. Let's consider how images are constructed in a thin lens.
Historical background
The first lenses known to the ancient Greeks and Romans were spherical glass vessels filled with water. These prototypes of modern optical glasses were used to start fires.
It was only at the end of the 13th century that the first glass lens was made in Europe. Since then, the process of their manufacture has not changed much. The only innovation was the use of tar by Isaac Newton in the 17th century to polish the surfaces of optical objects.
Collecting and scattering optical glasses
To make it easier to understand the construction of images in a thin lens, considerthe question is, what are optical glasses. In general, there are only two types of lenses, which differ in their shape and ability to refract the light flux. The following types are distinguished:
- Converging lenses. This type has a thickness of its central part greater than the thickness of the edges. The resulting image in a converging lens is formed on the other side of the light falling on it. This type has the ability to collect light into a single point (positive focus).
- Diverging lenses. Their central part is thinner than the edges. Due to their shape, these optical glasses scatter the light incident on them, which leads to the formation of an image on the same side of the lens as the rays from an object fall on it. The generated image is much smaller than the actual item. If the rays scattered by this optical glass are continued in such a way as to determine their origin, then it will seem that they emerge from one point in front of it. This point is called the focus, which is negative or imaginary for a diverging lens.
Different shapes of optical glasses
The existing two types of lenses can be made in several ways. The following 6 forms are distinguished:
- Biconvex.
- Plano-convex.
- With a convex meniscus (concave-convex).
- Biconcave.
- Plano-concave.
- With a concave meniscus (convex-concave).
Convex glass elements
To understand the physics of the lens and building inthin imaging lenses, it is necessary to know the basic elements of this optical object. Let's list them:
- The optical center (O) is the point through which light passes without being refracted.
- The main axis is a straight line that passes through the point of the optical center and the main focus.
- The main or main focus (F) is the point through which light rays or their extensions pass if they fall on optical glass parallel to its main axis.
- Auxiliary axis - any straight line that passes through the optical center.
- The radii of curvature are the two radii, R1 and R2, of the spheres that form the lens.
- Centers of curvature - two centers of spheres, C1 and C2, which form the surfaces of optical glass.
- Focal length (f) - the distance between the focal point and the optical center. There is another definition of the value (f): this is the distance from the center of the optical lens to the image, which gives an object located infinitely far away.
Optical properties
Whether it is a simple convex glass or complex optical systems, which are a collection of individual lenses, their optical properties depend on two parameters: the focal length and the relationship between the focal length and the diameter of the lens.
Focal length is measured in two ways:
- In units of normal distance, such as 10cm, 1m, and so on.
- In diopters, this is a value that is inversely proportional to the focal length, measured in meters.
For example, an optical glass with a power of 1 diopter has a focal length of 1 m, while a lens with a power of 2 diopters has a focal length of only 0.5 m.
The diameter of a lens and its relation to the focal length determines the ability of an optical glass to collect light or its light output.
Properties of rays passing through the lens
In 8th grade schools, building images in thin lenses is one of the important topics in physics. To learn how to build these images, one should know not only the basic concepts and elements, but also the properties of some rays passing through an optically active object:
- Any ray passing parallel to the main axis is refracted in such a way that either it passes through the focus (in the case of a converging lens), or its imaginary continuation passes through the focus (in the case of a divergent one).
- The beam that passes through the focus is refracted so that it continues its movement parallel to the main axis. Note that in the case of a diverging lens, this rule is valid if the continuation of the beam incident on it passes through the focus located on the other side of the optical object.
- Any ray of light that passes through the center of the lens does not experience any refraction and does not change direction.
Features of building images in thin lenses
Although collecting and scattering opticalglasses have similar properties, the construction of images in each of them has its own characteristics.
When constructing images, the thin lens formula is:
1/f=1/do+1/di, where do and di is the distance from the optical center to the object and to its image.
Note that the focal length (f) is positive for converging lenses and negative for diverging ones.
The application of the above properties of rays passing through a collecting optical glass leads to the following results:
- If the object is located at a distance of more than 2f, then a real image is obtained, which has a smaller size than the object. We see it upside down.
- An object placed at a distance of 2f from the lens results in a real inverted image of the same size as the object itself.
- If an object is at a distance of more than f, but less than 2f, then a real inverted and enlarged image of it is obtained.
- If the object is at the focal point, then the rays passing through the optical glass become parallel, which means there is no image.
- If an object is closer than one focal length, then its image will turn out to be imaginary, direct and larger than the object itself.
Since the properties of rays passing through a converging and diverging lens are similar, the construction of images given by a thin lens of this type is carried out according to similar rules.
Drawingsimaging for various occasions
In the drawings, a converging lens is indicated by a line at the ends of which there are arrows pointing outward, and a diverging lens is indicated by a line with arrows at the ends that are directed inward, that is, at each other.
Different variants of the drawings for constructing images in thin lenses, which were discussed in the previous paragraph, are shown in the figure below.
As can be seen from the figure, all images (for any type of optical glass and the location of the object relative to them) are built on two beams. One is directed parallel to the main axis, and the other passes through the optical center. The use of these beams is convenient because their behavior after passing through the lens is known. Also note that the lower edge of the object (red arrow in this case) is located on the main optical axis, so it is enough to build only the image of the top point of the object. If the object (red arrow) is located arbitrarily relative to the optical glass, then it is necessary to build an image of both its upper and lower parts independently.
Two beams are enough to build any images. If there is uncertainty about the result, then it can be checked using the third ray. It should be directed through the focus (in front of the converging lens and behind the diverging lens), then after passing through the optical glass and refraction in it, the beam will be parallel to the main optical axis. If the problem of building an image in a thin lens is solvedright, then it will pass through the point where the two main beams intersect.
The process of manufacturing optical objects
Most lenses are made from special types of glass called optical lenses. There are no internal stresses, air bubbles and other imperfections in such glass.
The process of making lenses takes place in several stages. First, a concave or convex object of the desired shape is cut out of a block of optical glass using appropriate metal tools. It is then polished using tar. At the final stage, the optical glass is resized using abrasive tools so that the center of gravity exactly coincides with the optical center.
Due to the development of technologies for obtaining and processing various types of plastic, lenses are now increasingly being made from transparent types of plastic, which are cheaper, lighter and less fragile than their glass counterparts.
Application areas
Optical glasses are used to solve various vision problems. For this, both plastic contact lenses and glass ones (with glasses) are used.
In addition, optical glasses are used in photographic cameras, microscopes, telescopes and other optical instruments. They use a whole system of lenses. For example, in the case of the simplest microscope, consisting of two optical glasses, the first one forms a real image of the object, andthe second is used to enlarge its image. Therefore, the second glass is located at an appropriate distance from the first, according to the rules for constructing images in a thin lens.
