Ray Optics

What are the physics of light? The best way to describe how light travels would be to use ray optics. Rays are basically infinitesimally thin slices of waves in the direction that they are traveling.

Reflection

Practically all objects reflect a certain portion of the light falling on them. The light that is reflected off an object is the color that the eyes see. If a ray of light hits a flat, shiny surface, than it reflects off at the same angle. This means the ray that hits the surface, called the incident ray, which has an angle of incidence from the normal (an imaginary line perpendicular to the surface at the point where the incident ray encounters it) bounces off as the reflected ray, which has an equal angle of reflection from the normal.

This is leads to the law of reflection which follows:

The incident ray, the reflected ray, and the normal to the surface all lie in the same plan, and the angle of reflection, , equals the angle of incidence, .

There are two types of reflection. Specular reflection is when parallel light rays strike a smooth, plane surface, such as in the figure below, and reflect off parallel. This is important in determining the properties of mirrors because it shows how much the mirror reflects without distortion. The other type of reflection, diffuse reflection, is when parallel rays strike a rough surface, causing them to reflect in all directions, causing distortion.

Images formed by a plane mirror

Looking into a plane mirror, you can see an image of yourself that has four fundamental properties:

1. The image is left to upright.
2. The image is the same size as you are.
3. The image is located as far behind the mirror as you are in front of it
4. The image is reversed left to right.

The image being reversed means that when you wave your right hand, the image seems to wave its left hand. The image you see that is behind the mirror is called the virtual image. Since the light rays do not really pass through the image, images formed by a plane mirror are known as virtual images. You can distinguish them from real images, which are formed by light that does pass through the image because a white piece of paper placed at the image location will not show anything if the image is virtual, but will show the image if the image is real.

Parabolic mirrors

A parabolic mirror is a common type of curved mirror. In general shape, the mirror is roughly a section of the surface of a sphere, though as the name suggests, the curve is not perfectly spherical. It is parabolic. There are two types of parabolic mirrors: concave and convex. Imagine a parabola with the inside surface (the part on the inside of the curve) as a reflective surface. This is a concave parabolic mirror. Conversely, a parabola with the outside as a reflective surface is a convex parabolic mirror.

The law of reflection applies two both these types of mirrors as it did with the plane mirror. Only now the normal is drawn perpendicular to the mirror at the point of incidence, which is where the ray strikes the surface of the mirror. Both these types of mirrors have a vertex, shown on the diagram. The line perpendicular to the surface of the mirror at the vertex is called the principal axis.

The figure above shows how an object (the red shape above the principle axis) forms an image (the red shape below the principle axis) in a concave parabolic mirror, and also labels certain special distances. As you can see, the ray parallel to the principle axis goes through a point labeled F. This is the focal point of the mirror. All rays of light parallel to the principle axis reflecting off the surface of the mirror will go through this point. Similarly, you can see that a ray going through the focal point will be reflected back parallel to the principal axis.The focal length of the mirror, f, is the distance from the focus to the vertex. The height of the object is otherwise stated ho, while the height of the image is hi. The distance from the object to the vertex is do, and, similarly the distance from the image to the vertex is di. Finally, the distance from the object to the focal point F is so, and the distance from the image to the focus is si. We label all these distances for ease in use, because there are many useful relationships between them, which follow.

as well as

Refraction

Light will always travel in the fastest path from point A to point B. If this path goes through different materials through which light travels at different speeds, then light will not travel in a straight line. This bending of light when it enters a new medium is known as refraction, and is the reason a stick looks bent when we hold part of it in water. Our eyes are trained to think that light travels to us in a straight line, so when it bends, we think it is the object that is bent, not the light.

Light travels faster in media that are less optically dense and slower in media that are more optically dense. The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in the medium, and is represented by the letter n.

This index of refraction is quite important, because we can use it to determine at what angle the light bends. We do this using an equation developed by Wilebrord Snell, named, aptly enough, Snell's law. When light hits the boundary between two transparent media, it generally splits into two parts. One part reflects back into the first medium, the other refracts into the second media. The exception to this is when the light hits at such an angle that there is total internal reflection, which means that all the light bounces back into the original medium. Snell's law of refraction states that when light travels from a medium with a refractive index of into a medium with a refractive index of , the incident ray, normal ray, and reflected ray all lie in the same plane. Furthermore, (the angle of incidence) and (the angle of refraction are related by the following formula:

sin = sin

The speed of light in air is so close to the speed of light in a vacuum, that for most purposes we can use a value of one for the index of refraction of air. Light travels more noticeabley slowly in some other materials, however, and a table of some of these values follows. Of course, light can never travel faster than c, its speed in a vacuum, which is m/s.

 Substance (at 20° C) Index of refraction, n Diamond 2.419 Sodium Chloride 1.544 Water 1.333 Benzene 1.501

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