There are objects that are capable of changing the density of the electromagnetic radiation flux incident on them, that is, either increasing it by collecting at one point, or decreasing it by scattering. These objects are called lenses in physics. Let us consider this question in more detail.
What are lenses in physics?
By this concept is meant absolutely any object that is capable of changing the direction of propagation of electromagnetic radiation. This is a general definition of lenses in physics, which includes optical glasses, magnetic and gravitational lenses.
In this article, the main attention will be paid to optical glasses, which are objects made of a transparent material, and limited to two surfaces. One of these surfaces must necessarily have curvature (that is, be part of a sphere of finite radius), otherwise the object will not have the property of changing the direction of propagation of light rays.
The principle of the lens
The essence of this simple optical object is the phenomenon of refraction of sunlight. At the beginning of the XVII century, the famous Dutch physicist and astronomer Willebord Snell van Royen published the law of refraction, which now bears his last name. The wording of this law is as follows: when sunlight passes through the interface between two optically transparent media, the product of the sine of the angle of incidence between the beam and the normal to the surface and the refractive index of the medium in which it propagates is constant.
To clarify the foregoing, we give an example: let light fall on the surface of the water, while the angle between the normal to the surface and the beam is θ 1 . Then, the light beam refracts and begins to propagate in water already at an angle θ 2 to the normal to the surface. According to Snell’s law, we obtain: sin (θ 1 ) * n 1 = sin (θ 2 ) * n 2 , here n 1 and n 2 are the refractive indices for air and water, respectively. What is the refractive index? This value shows how many times the speed of propagation of electromagnetic waves in a vacuum is greater than that for an optically transparent medium, i.e. n = c / v, where c and v are the speeds of light in a vacuum and in a medium, respectively.
The physics of the occurrence of refraction consists in the fulfillment of the Fermat principle, according to which light moves in such a way as to overcome the distance from one point to another in space in the least amount of time.
Types of Lenses
The type of optical lens in physics is determined solely by the shape of the surfaces that form it. The direction of refraction of the ray incident on them depends on this form. So, if the surface curvature is positive (convex), then upon exit from the lens the light beam will propagate closer to its optical axis (see below). Conversely, if the surface curvature is negative (concave), then after passing through the optical glass, the beam will begin to move away from its central axis.
We note once again that the surface of any curvature refracts the rays in the same way (according to Stell's law), but the normals to them have a different slope relative to the optical axis, resulting in different behavior of the refracted beam.
A lens that is bounded by two convex surfaces is called a collection lens. In turn, if it is formed by two surfaces with negative curvature, then it is called scattering. All other types of optical glasses are associated with a combination of these surfaces, to which a plane is also added. What property a combined lens will have (scattering or collecting) depends on the total curvature of the radii of its surfaces.
Lens elements and ray properties
To build in lenses in the physics of images, you need to get acquainted with the elements of this object. They are listed below:
- The main optical axis and center. In the first case, they mean a straight line passing perpendicular to the lens through its optical center. The latter, in turn, is a point inside the lens, passing through which the beam does not experience refraction.
- Focal length and focus - the distance between the center and the point on the optical axis, into which all the rays incident on the lens are collected parallel to this axis. This definition is true for collecting optical glasses. In the case of scattering lenses, the rays themselves will not be collected at the point, but their imaginary continuation. This point is called the main focus.
- Optical power. This is the name of the reciprocal of the focal length, that is, D = 1 / f. It is measured in diopters (diopters), that is, 1 diopters. = 1 m -1 .
The following are the basic properties of the rays that pass through the lens:
- the beam passing through the optical center does not change the direction of its motion;
- rays incident parallel to the main optical axis change their direction so that they pass through the main focus;
- rays incident on the optical glass at any angle, but passing through its focus, change their propagation direction in such a way that they become parallel to the main optical axis.
The above properties of rays for thin lenses in physics (as they are called, because it does not matter what spheres they are formed and how thick they are, only the optical properties of the object matter) are used to construct images in them.
Images in optical glasses: how to build?
The figure below shows in detail the schemes for constructing images in the convex and concave lenses of an object (red arrow), depending on its position.
From the analysis of the diagrams in the figure, important conclusions follow:
- Any image is built on just 2 rays (passing through the center and parallel to the main optical axis).
- The collecting lenses (indicated with arrows pointing outward) can produce both enlarged and reduced images, which in turn can be real (real) or imaginary.
- If the subject is in focus, the lens does not form its image (see the lower diagram on the left in the figure).
- Scattering optical glasses (indicated by arrows at their ends directed inward) give, regardless of the position of the subject, an always reduced and imaginary image.
Finding the distance to the image
To determine at what distance the image appears, knowing the position of the object itself, we give the lens formula in physics: 1 / f = 1 / d o + 1 / d i , where d o and d i are the distance to the object and to its image from the optical center, respectively, f is the main focus. If we are talking about collecting optical glass, then the number f will be positive. Conversely, for a scattering lens, f is negative.
We use this formula and solve a simple problem: let the object be at a distance d o = 2 * f from the center of the collecting optical glass. Where will his image appear?
From the conditions of the problem we have: 1 / f = 1 / (2 * f) + 1 / d i . Where: 1 / d i = 1 / f - 1 / (2 * f) = 1 / (2 * f), that is, d i = 2 * f. Thus, the image appears at a distance of two foci from the lens, but on the other hand than the subject itself (this is indicated by the positive sign of the value of d i ).
Short story
It is interesting to cite the etymology of the word "lens". It originates from the Latin words lens and lentis, which means “lentil,” since optical objects in their shape really look like the fruit of this plant.
The refractive power of spherical transparent bodies was known to the ancient Romans. For this purpose, they used round glass vessels filled with water. Glass lenses themselves began to be manufactured only in the 13th century in Europe. They were used as a tool for reading (modern glasses or a magnifier).
The active use of optical objects in the manufacture of telescopes and microscopes dates back to the 17th century (Galileo invented the first telescope at the beginning of this century). Note that the mathematical formulation of the Stella law of refraction, without knowledge of which it is impossible to manufacture lenses with desired properties, was published by a Dutch scientist at the beginning of the same XVII century.
Other types of lenses
As noted above, in addition to optical refractive objects, there are also magnetic and gravitational ones. An example of the former is magnetic lenses in an electron microscope, a striking example of the latter is to distort the direction of the light flux when it passes near massive cosmic bodies (stars, planets).