Engineering in Kenya

# Geometric Optics

Posted by on Dec 16, 2017 in Physics | 0 comments

Geometric optics it is the study of light waves in different type of environment. Geometric optics is concerned with the images that result when spherical waves fall on flat and spherical surfaces. Geometric optics helps to understand how images can be formed either by reflection or by refraction and how mirrors and lenses work because of reflection and refraction. Form the ray approximation it is known that light travels in straight lines. Both of these steps lead to valid predictions in the field called geometric optics the objects of study in the field of wave optics. Read more articles in Engineering in Kenya

# Principles of Geometric optics

The simple geometric optics techniques are used to examine the properties of the images formed by flat or spherical surfaces. Approximations of geometrical optics which use ray model of light; is used to analyze the formation of images by assuming the light to travel in straight line paths or rays whereby rays are drawn perpendicular to the wave front in a direction the travel of the wave. In 1678, Christian Huyghens suggested a simple theory of light as a wave. This wave theory of light constitutes a technique for describing wave motion. Huyghens ‘theory is based on a geometrical construction that enables us to know where a given wave front will be at any time in the future if we know its present position which is also the geometric optics.

In geometric optics the Huyghens principle can be used to derive geometrically the laws of reflection and refraction. The Huyghens’ principle which states that, all points of a wave front can be considered as a source of secondary spherical wavelets which spread out in all directions, show that the angle of incidence is equal to the angle of reflection (θi = θ’r )  which forms the law of reflection in geometric optics. The principle is the Fermat’s principle which state that a light of ray travelling from one fixed point to another fixed point follow a path such that compared with a nearby path , the time required is either minimal or maximum or remain unchanged that is, stationary also used in the derivation of image in geometric optics.

## Images in Geometric Optics

Ideally, geometric optics is generally concerned with the images that result when spherical waves falling on flat and spherical surfaces. There are two types of mirrors the flat mirror and the spherical mirror used in geometric optics. Using geometric construction to locate the image of an object placed in front of a flat mirror the image formed by reflection from a flat mirror is located behind the mirror a perpendicular distance from the mirror which is the image distance and the image distance has the same magnitude as the object distance. The image has the following properties; the image is as far behind the mirror as the object is in front of the mirror, the image is unmagnified, virtual, and upright and the image has front back reversal.

The other type of mirror in geometric optics is the spherical mirrors which are two type the concave and the convex. A spherical mirror, as its name implies, has the shape of a section of a sphere. A mirror, in which light is reflected from the inner, concave surface, is called a concave mirror. The rays from the object when they the surface of a concave mirror tends to converge at the image point and the image formed is always inverted and is a real image formed in front of the mirror from the geometric construction in geometric optics.

The geometric construction in geometric optics to find formation of an image by a convex mirror that is, one silvered so that light is reflected from the outer, convex surface, shows that the ray of light from the object tend to diverge . This is sometimes called a diverging mirror because the rays from any point on an object diverge after reflection as though they were coming from some point behind the mirror. Furthermore, the image is always upright, smaller than the object and virtual because the reflected rays only appear to originate at the image point. This type of mirror is often used in stores to foil shoplifters as single mirror can be used to survey a large field of view because it forms a smaller image of the interior of the store one of the application in the field of geometric optics.

The other study of image formation in geometric optics is due to refraction which occurs in lenses. The image formed by one refracting surface serves as the object for the second surface in the lenses which are applied in many optical instruments.

### Application of Geometric Optics

The concept of geometric optics has a lot of application in the society whereby it is used in optical instrument and devices. They are designed to produce magnified images of objects whereby the small objects appear large such as in a microscope and distant objects appear close such as in a telescope. For example the optical microscopes let us see objects as small as 0.1µm in diameter of other application of geometric optics.

The magnifying glass or simple microscope is the simplest magnifying instrument using the concept of geometric optics. It is a single converging lens: the object is placed between the center and the first focal point and the image formed is virtual, upright and this image appears on the retina larger than that observed by the unaided eye. The camera itself is an example of application of optical instrument using the concept of geometric optics. It consists of a light tight box, a converging lens that produces a real image, and a film behind the lens to receive the image by focusing the camera by varying the distance between lens and film.

Ideally, like a camera, a normal eye focuses light and produces a sharp image using also the concept of geometric optics. However, the mechanisms by which the eye controls the amount of light admitted and adjusts to produce correctly focused images are far more complex, intricate, and effective than those in even the most sophisticated camera and in all respects, the eye a physiological wonder of the geometric optics. The condition is known as farsightedness or hyperopia whereby a person can usually see far away objects clearly but not nearby objects is corrected by placing a converging lens in front of the eye. A person with nearsightedness or myopia, another mismatch condition, where a person can focus on nearby objects but not on faraway objects is corrected with a diverging lens another important application of geometric optics.

Other application of geometric optics is the microscope and the telescope which were developed at about the same time in the early 1600s. A typical compound microscope consists of a tube with a converging lens at one end and the lens close to the object being viewed called objective lens. Observations and drawing of magnified cells thanks to the use of powerful microscopes contributed to the understanding of biological processes among other useful contribution of geometric optics.