Geometric optics is a special branch 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's take a closer look at these laws in the article, and also give examples of their use in practice.
Ray 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 (phenomena of the photoelectric effect and light pressure). Geometric optics, as noted in the introduction, deals only with the laws of light propagation, without delving into their nature.
If the beam moves in a homogeneous transparent medium or in a vacuum and does not encounter any obstacles on its way, then the light beam will move in a straight line. This feature led to the formulation of the principle of least time (Fermat's principle) by the Frenchman Pierre Fermat in the middle of the 17th century.
Another important feature of light rays is their independence. This means that each ray propagates in space without "feeling"another beam without interacting with it.
Finally, the third property of light is the change in the speed of its propagation when moving from one transparent material to another.
The marked 3 properties of light rays are used in the derivation of the laws of reflection and refraction.
Reflection phenomenon
This physical phenomenon occurs when a light beam hits an opaque obstacle much larger than the wavelength of light. The fact of reflection is a sharp change in the trajectory of the beam in the same medium.
Assume that a thin beam of light falls on an opaque plane at an angle θ1 to the normal N drawn to this plane through the point where the beam hits it. Then the beam is reflected at a certain angle θ2 to the same normal N. The phenomenon of reflection obeys two main laws:
- The incident reflected beam of light and the N normal lie in the same plane.
- The angle of reflection and the angle of incidence of a light beam are always equal (θ1=θ2).
Application of the phenomenon of reflection in geometric optics
The laws of reflection of a light beam are used when constructing images of objects (real or imaginary) in mirrors of various geometries. The most common mirror geometries are:
- flat mirror;
- concave;
- convex.
It's quite easy to build an image in any of them. In a flat mirror, it always turns out to be imaginary, has the same size as the object itself, is direct, in itthe left and right sides are reversed.
Images in concave and convex mirrors are built using several rays (parallel to the optical axis, passing through the focus and through the center). Their type depends on the distance of the object from the mirror. The figure below shows how to build images in convex and concave mirrors.
The phenomenon of refraction
It consists in a break (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 that is not equal to 90o.
The modern mathematical description of this phenomenon was made by the Dutchman Snell and the Frenchman Descartes at the beginning of the 17th century. Denoting the angles θ1 and θ3 for the incident and refracted rays relative to the normal N to the plane, we write a mathematical expression for the phenomenon of refraction:
1sin(θ1)=n2sin(θ 3).
The quantities n2and n1are 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 of n is a function of the frequency of light (n is greater for higher frequencies than for lower ones).
Application of the phenomenon of refraction in geometric optics
The described phenomenon is used to build images inthin lenses. A lens is an object made of a transparent material (glass, plastic, etc.) that is bounded by two surfaces, at least one of which has non-zero curvature. There are two types of lenses:
- gathering;
- scattering.
Converging 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. Scattering surfaces are formed by concave transparent surfaces, so after the passage of parallel rays through them, light is scattered.
Construction of images in lenses in 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 obtained images 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 operating according to the laws of geometric optics
The simplest of them is a magnifying glass. It is a single convex lens that magnifies real objects up to 5 times.
A more sophisticated device, which is also used to magnify objects, is a microscope. It already consists of a lens system (at least 2 converging lenses) and allows you to get an increase inseveral hundred times.
Finally, the third important optical instrument is a telescope used to observe celestial bodies. It can consist of both a lens system, then it is called a refractive telescope, and a mirror system - a reflective telescope. These names reflect the principle of its work (refraction or reflection).
