Geometric optics is a special section of physical optics, which does not deal with the nature of light, but studies the laws of motion of light rays in transparent media. Let us consider these laws in more detail in the article, as well as give examples of their use for practice.
Beam Propagation in Homogeneous Space: Important Properties
Everyone knows that light is an electromagnetic wave, which for some natural phenomena can behave like a stream of energy quanta (photoelectric effect and light pressure phenomena). Geometric optics, as noted in the introduction, deals only with the laws of the propagation of light, not delving into their nature.
If the beam moves in a uniform transparent medium or in a vacuum and does not encounter any obstacle, then the course of the light beam will be observed in a straight line. This feature led to the formulation in the middle of the XVII century by the French Pierre Fermat of the principle of least time (Fermat's principle).
Another important feature of light rays is their independence. This means that each ray propagates in space, “not feeling” the other ray, without interacting with it.
Finally, the third property of light is the change in the speed of its propagation during the transition from one transparent material to another.
The noted 3 properties of light rays are used in deriving the laws of reflection and refraction.
Reflection phenomenon
This physical phenomenon occurs when a light ray hits an opaque obstacle that is much larger than the wavelength of light. The fact of reflection is a sharp change in the path of the beam in the same medium.
Suppose that a thin beam of light falls on an opaque plane at an angle θ 1 to the normal N drawn to this plane through the point of incidence of the beam on it. Then the beam is reflected at a certain angle θ 2 to the same normal N. The phenomenon of reflection obeys two main laws:
- The incident reflected light beam and the N normal lie in the same plane.
- The angle of reflection and the angle of incidence of the light beam are always equal (θ 1 = θ 2 ).
The use of the reflection phenomenon in geometric optics
The laws of reflection of a light beam are used in constructing images of objects (real or imaginary) in mirrors of various geometries. The most common mirror geometries are as follows:
- flat mirror;
- concave;
- convex.
In any of them, building an image is quite simple. In a flat mirror, it always turns out to be imaginary, has the same size as the object itself, is straight, in it the left and right sides are swapped.
Images in concave and convex mirrors are constructed using several beams (parallel to the optical axis, passing through the focus and through the center). Their type depends on the distance of the object to the mirror. The figure below shows how to build images in convex and concave mirrors.
Refraction phenomenon
It consists in the fracture (refraction) of the beam when it crosses the boundary of two different transparent media (for example, water and air) at an angle to the surface, not equal to 90 o .
A modern mathematical description of this phenomenon was made by the Dutch Snell and the French Descartes at the beginning of the XVII century. Denoting the angles θ 1 and θ 3 for the incident and refracted rays relative to the normal N to the plane, we write the mathematical expression for the refraction phenomenon:
n 1 * sin (θ 1 ) = n 2 * sin (θ 3 ).
The values of n 2 and n 1 are the refractive indices of media 2 and 1. They show how much the speed of light in the medium differs from that in airless space. For example, for water n = 1.33, and for air - 1,00029. You should know that the value n is a function of the frequency of light (for large frequencies, n is greater than for smaller ones).
Application of the phenomenon of refraction in geometric optics
The described phenomenon is used to construct images in thin lenses. A lens is an object made of a transparent material (glass, plastic and others), which is limited to two surfaces, and at least one of them has a non-zero curvature. Lenses are of two types:
The collecting lenses are formed by a convex spherical (spherical) surface. The refraction of light rays in them occurs in such a way that they collect all parallel rays at one point - the focus. The scattering particles are formed by concave transparent surfaces, therefore, after passing parallel rays through them, light scatters.
The construction of images in lenses by its technique is similar to the construction of images in spherical mirrors. It is also necessary to use several beams (parallel to the optical axis passing through the focus and through the optical center of the lens). The nature of the images obtained is determined by the type of lens and the distance of the object to it. The figure below shows the technique for obtaining images of an object in thin lenses for various cases.
Devices working according to the laws of geometric optics
The simplest one is a magnifier. It is a single convex lens, which serves to increase real objects up to 5 times.
A more complex instrument, which is also used to enlarge objects, is a microscope. It already consists of a lens system (at least 2 collecting) and allows you to get an increase of several hundred times.
Finally, the third important optical instrument is the telescope used to observe celestial bodies. It can consist of a system of lenses, then it is called refractive, and of a system of mirrors - a reflex telescope. These names reflect the principle of its work (refraction or reflection).