Lenses are transparent objects that are capable of refracting sunlight. They are made mainly of glass. The words "refract light" means the ability to change the direction of propagation of incident light rays. Consider how the construction of images in a thin lens is carried out.
History reference
The first lenses that were known to the ancient Greeks and Romans were spherical glass vessels filled with water. These prototypes of modern optical glasses were used to kindle fire.
Only at the end of the 13th century was the first glass lens made in Europe. Since then, the manufacturing process has not changed much. The only innovation was the use of tar in the 17th century by Isaac Newton 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, we consider the question of what kind of optical glasses are. In the general case, there are only two types of lenses, which differ in their shape and ability to refract light flux. The following types are distinguished:
- Collecting lenses. This type has a thickness of its central part greater than the thickness of the edges. The resulting image in the collecting lens is formed on the other side of the incident light. This type has the ability to collect light at one point (positive focus).
- Scattering 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 onto which rays from an object fall. The generated image is much smaller than the real subject. If the rays scattered by this optical glass are continued to determine their origin, then it will seem that they are coming out of one point in front of it. This point is called the focus, which is negative or imaginary for the scattering lens.
Different shapes of optical glasses
The existing two types of lenses can be made in several ways. The following 6 forms are distinguished:
- Lenticular.
- Flat convex.
- With a convex meniscus (concave-convex).
- Biconcave.
- Flat concave.
- With a concave meniscus (convex-concave).
Convex Glass Elements
To understand the physics of the lens and the construction of images in thin lenses, it is necessary to know the basic elements of this optical object. We 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 the rays of light or their continuations pass if they fall on the optical glass parallel to its main axis.
- The auxiliary axis is any straight line that passes through the optical center.
- The radii of curvature are two radii, R 1 and R 2 , of the spheres forming the lens.
- The centers of curvature are the two centers of the spheres, C 1 and C 2 , which form the surfaces of the optical glass.
- Focal length (f) is 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.
Optical properties
Whether we are talking about simple convex glass or complex optical systems, which are a combination 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, for example, 10 cm, 1 m 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 having an optical power of 1 diopter has a focal length of 1 m, and a lens with an optical power of 2 diopters has a focus distance of only 0.5 m.
The diameter of the lens and its relation to the focal length determine the ability of an optical glass to collect light or its light power.
Properties of rays passing through the lens
In schools in the 8th grade, building thin-lens images 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:
- Every ray passing parallel to the main axis is refracted in such a way that it either passes through the focus (in the case of a collecting lens), or through its focus passes its imaginary extension (in the case of the scattering lens).
- A ray that passes through the focus is refracted so that it continues to move further parallel to the main axis. Note that in the case of a scattering lens, this rule is valid if the continuation of the incident beam 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 the direction of its movement.
Features of construction in thin image lenses
Although collecting and scattering optical glasses have similar properties, the construction of images in each of them has its own characteristics.
When constructing images, the formula of a thin lens has the form:
1 / f = 1 / d o + 1 / d i ,
where d o and d i - the distance from the optical center to the object and to its image.
Note that the focal length (f) is a positive value for collecting lenses and negative for scattering lenses.
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 valid image is obtained having a smaller size than the object. We see him upside down.
- An object located 2f from the lens results in a real inverted image of the same size as the object itself.
- If the subject is at a distance of more than f, but less than 2f, then we get a real inverted and enlarged image.
- If the subject is at the focal point, then the rays passing through the optical glass become parallel, which means the absence of any image.
- If the subject is closer than one focal length, then its image will turn out to be imaginary, direct and larger than the subject itself.
Since the properties of the rays passing through the collecting and scattering lenses are similar, the construction of images produced by a thin lens of this type is carried out according to similar rules.
Drawings for building images for various occasions
In the drawings, a collecting lens is indicated by a line at the ends of which there are arrows pointing outward, and a diffusing lens is indicated by a line with arrows at the ends that are directed inward, that is, towards each other.
Various versions of the construction drawings in the thin lenses of the images 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 glasses 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 rays is convenient, since their behavior after passing through the lens is known. Also note that the lower edge of the object (the red arrow in this case) is located on the main optical axis, so it’s enough to construct only the image of the upper point of the object. If the object (the red arrow) is located arbitrarily relative to the optical glass, then it is necessary to build an image of both the upper and lower parts of it independently.
Two rays to build any image is enough. 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 collecting lens and behind the scattering lens), then after passing the optical glass and refracting in it, the beam will be parallel to the main optical axis. If the task of constructing an image in a thin lens is correctly solved, then it will go through the point where the two main rays intersect.
The process of manufacturing optical objects
Most lenses are made from special types of glass called optical. In such a glass there are no internal stresses, air bubbles and other imperfections.
The process of manufacturing lenses takes place in several stages. First, a concave or convex object of the desired shape is cut out from the optical glass block using appropriate metal tools. Then it is subjected to polishing using tar. At the final stage, the dimensions of the optical glass are changed using abrasive tools so that the center of gravity exactly matches the optical center.
In connection with the development of technologies for the production and processing of various types of plastics, lenses are now increasingly being made from transparent types of plastic, which are cheaper, lighter and less fragile than their glass counterparts.
Fields of application
Optical glasses are used to solve various vision problems. For this, both plastic contact lenses and glass (with glasses) are used.
In addition, optical glasses are used in photographic cameras, microscopes, telescopes and other optical devices. They use a whole system of lenses. For example, in the case of the simplest microscope, consisting of two optical glasses, the first forms a real image of the object, and the 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.