Light

The Electromagnetic and Visible Spectra
Electromagnetic waves are capable of transporting energy through the vacuum of outer space. Electromagnetic waves are produced by a vibrating electric charge and as such, they consist of both an electric and a magnetic component.
Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as the electromagnetic spectrum. The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter. The diagram below depicts the electromagnetic spectrum and its various regions. The longer wavelength, lower frequency regions are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right. Two very narrow regions within the spectrum are the visible light region and the X-ray region. You are undoubtedly familiar with some of the regions of the electromagnetic spectrum.
Visible Light Spectrum
Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band. Since this narrow band of wavelengths is the means by which humans see, we refer to it as the visible light spectrum. Normally when we use the term "light," we are referring to a type of electromagnetic wave which stimulates the retina of our eyes. In this sense, we are referring to visible light, a small spectrum from the enormous range of frequencies of electromagnetic radiation. This visible light region consists of a spectrum of wavelengths which range from approximately 700 nanometers (abbreviated nm) to approximately 400 nm. Expressed in more familiar units, the range of wavelengths extends from 7 x 10-7 meter to 4 x 10-7 meter. Each individual wavelength within the spectrum of visible light wavelengths is representative of a particular color.
That is, when light of that particular wavelength strikes the retina of our eye, we perceive that specific color sensation. Isaac Newton showed that light shining through a prism will be separated into its different wavelengths and will thus show
the various colors that visible light is comprised of. The separation of visible light into its different colors is known as dispersion. Each color is characteristic of a distinct wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. For these reasons, visible light is dispersed upon passage through a prism .. The red wavelengths of light are the longer wavelengths and the violet wavelengths of light are the shorter wavelengths. Between red and violet, there is a continuous range or spectrum of wavelengths.
When all the wavelengths of the visible light spectrum strike your eye at the same time, white is perceived. The sensation of white is not the result of a single color of light. Rather, the sensation of white is·the result of a mixture of two or more colors of light. Thus, visible light - the mix of ROYGBIV - is sometimes referred to as white light. Technically speaking, white is not a color at all - at least not in the sense that there is a light wave with a wavelength which is characteristic of white. Rather, white is the combination of all the colors of the visible light spectrum. If all.the wavelengths of the visible light spectrum give the appearance of white, then none of the wavelengths would lead to the appearance of black. Once more, black is not actually a color. Technically- speaking, black is merely the absence of the wavelengths of the visible light spectrum. So when you are in a room with no lights and everything around you apRears black, it means that there are no wavelengths of visible light striking your eye as you sight at the surroundings.
Color addition
The subject of color perception can be simplified if we think in terms of primary colors of light. We have already learned that white is not a color at all, but rather the presence of all the frequencies of visible light. When we speak of white light, we are referring to ROYGBIV - the presence of the entire spectrum of visible light. But combining the range of frequencies in the visible light spectrum is not the only means of producing while light. White light can also be produced by combining only three distinct frequencies of light, provided that they are widely separated on the visible light spectrum. Any three colors (or frequencies) of light which produce white light when combined with the correct intensity are called primary colors of light. There are a variety of sets of primary colors. The most common set of primary colors is red (R), green (G) and blue (B). When red, green and blue light are mixed or added together with the proper intensity, white (W) light is obtained. This is often represented by the equation below:
R + G + B = W
In fact, the mixing together (or addition) of two or three of these three primary colors of light with varying degrees of intensity can produce a wide range of other colors. For this reason, many television sets and computer monitors produce the range of colors on the monitor by the use of red, green and blue light-emitting phosphors.
R + G = Y
R + B = M
G + B = C
Yellow (Y), magenta (M) and cyan (e) are sometimes referred to as secondary colors of light since they are produced by the addition of equal intensities of two primary colors of light. The addition of these three primary colors of light with varying degrees of intensity will result in the countless other colors which we are familiar (or unfamiliar) with.
Complementary Colors of Light
Any two colors of light which when mixed together in equal intensities produce white are said to be complementary colors of each other. The complementary color of red light is cyan light. This is reasonable since cyan light is the combination of blue and green light; and blue and green light when added to red light will produce white light. Thus, red light and cyan light (blue + green) represent a pair of complementary colors; they add together to produce white light. This is illustrated in the equation below:
R + C = R + (B + G) = White
Each primary color of light has secondary color of light as its complement. The three pairs of complementary colors are listed below.
Complementary colors of Light
Red and Cyan
Green and Magenta
Blue and Yellow
The production of various colors of light by the mixing of the three primary colors of light is known as color addition. color addition to determine why different objects look specific colors when illuminated with various colors of light.
Blue Skies and Red Sunsets
We will attempt to answer these two questions:
Why are the skies blue?
Why are the sunsets red?
The interaction of sunligh with matter can result in one of three wave behaviors: absorption, transmission, and reflection. The atmosphere is gaseous sea which contains a variety of types of particles; the two most common types of matter present in the atmosphere are gaseous nitrogen and oxygen. These particles are most effective in scattering the higher frequency and shorter wavelength portions of the visible light spectrum. This scattering process involves the absorption of a light wave by an atom followed by reemission of a light wave in a variety of directions. The amount of multidirectiohnal scattering which occurs is dependent upon the frequency of the light. Atmospheric nitrogen and oxygen scatter violet light most easily, followed by blue light, green light, etc. So as white light (Roygbiv) from the sun passed through our atmosphere, the high frequencies (BIV) become scattered by atmospheric particles while the lower frequencies (ROY) are most likely to pass through the atmosphere without a significant alteration in their direction. This scattering of the higher frequencies of light illuminates the skies with light on the BIV end of the visible spectrum. Compared to blue light, violet light is most easily scattered by atmospheric particles. However, our eyes are more sensitive to light with blue frequencies. Thus, we view the skies as being blue in color.
Meanwhile, the light that is not scattered is able to pass through our atmosphere and reach our eyes in a rather non-interrupted path. The lower frequencies of sunlight (ROY) tend to reach our eyes as we sight directly at the sun during midday. While sunlight consists of the entire range of frequencies of visible light, not all frequencies are equally intense. In fact, sunlight tends to be most rich with yellow light frequencies. For these reasons, the sun appears yellow during midday due to the direct passage of dominant amounts of yellow frequencies through our atmosphere and to our eyes.
The appearance of the sun changes with the time of day. While it may be yellow during midday, it is often found to gradually turn color as it approaches sunset. This can be explained by light scattering. As the sun approaches the horizon line, sunligh must traverse a greater distance through our atmosphere
As the p!lth which sunlight takes through our atmosphere increases in length, ROYGBIV encounters more and more atmospheric particles. This results in the scattering of greater and greater amounts of yellow light. During sunset hours, the light passing through our atmosphere to our eyes tends to be most concentrated with red and orange frequencies of light. For this reason, the sunsets have a reddish-orange hue. The affect of a red sunset becomes more pronounced if the atmosphere contains more and more particles. The presence of sulfur aerosols (emitted as an industrial pollutant and by volcanic activity) in our atmosphere contributes to some magnificent sunsets (and some very serious environmental problems).
The objects which we see can be placed into one of two categories: luminous objects and illuminated objects. Luminous objects are objects which generate their own light. Illuminated objects are objects which are capable of reflecting light to our eyes. The sun is an example of a luminous object, while the moon is an illuminated object.
None of us are light-generating objects. We are not brilliant objects like the sun; rather, we are illuminated objects like the moon. We make our presence visibly known by reflecting light to the eyes of those who look our way. It is only by reflection that we, as well as most of the other objects in our physical world, can be seen.
The Law of Reflection
Light is known to behave in a very predictable manner. If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable law known as the law of reflection. The diagram below illustrates the law of reflection.
In the diagram, the ray of light approaching the mirror is known as the incident ray (labeled I in the diagram). The ray of light which leaves the mirror is known as the reflected ray (labeled R in the diagram). At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. This line is known as a normal line (labeled N in the diagram). The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection. (These two angles are labeled with the Greek letter "theta-r" for angle of reflection.) The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.
Specular vs. Diffuse Reflection
Reflection off of smooth surfaces such as mirrors or a calm body of water leads to a type of reflection known as specular reflection. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as diffuse reflection. Whether the surface is microscopically rough or smooth has a tremendous impact upon the subsequent reflection of a beam of light. The diagram below depicts two beams of light incident upon a rough and a smooth surface.
A light beam can be thought of as a bundle of individual light rays which are traveling parallel to each other. Each individual light ray of the bundle follows the law of reflection. If the bundle of light rays is incident upon a smooth surface, then the light rays reflect and remain concentrated in a bundle upon leaving the surface. On the other hand, if the surface is microscopically rough, the light rays will reflect and diffuse in many different directions.
Applications of Specular and Diffuse Reflection
There are several interesting applications of this distinction between specular and diffuse reflection. One application pertains to the relative difficulty of night driving on a wet asphalt roadway compared to a dry asphalt roadway. Most drivers are aware of the fact that driving at night on a wet roadway results in an annoying glare from oncoming headlights. The glare is the result of the specular reflection of the beam of light from an oncoming car. Normally a roadway would cause diffuse reflection due to its rough surface. But if the surface is wet, water can fill in the crevices and smooth out the surface. Rays of light from the beam of an oncoming car hit this smooth surface, undergo specular reflection and remain concentrated in a beam. The driver perceives an annoying glare caused by this concentrated beam of reflected light.
A second application of the distinction between diffuse and specular reflection pertains to the field of photography. Many people have witnessed in person or have seen a photograph of a beautiful nature scene captured by a photographer who set up the shot whit a calm body of water in the foreground. The water (if calm) provides for the specular reflection of light from the subject of the photograph. Light from the subject can reach the camera lens directly or it can take a longer path in which it reflects off the water before traveling to the lens. Since the light reflecting off the water undergoes specular reflection, the incident rays remain concentrated (instead of diffusig). The light is thus able to travel toghether ot the lens of the camer and produce an image (an exact replica) of the subject which is strong enough to perceive in the photograph. An example of such a photograph is shown below.
Right Angle Mirrors
there are optical systems which consist of two or more mirrors. One such system which is often found in homes is a pair of plane mirrors adjoined at right angles to each other. Such a system is called a right angle mirror.
If you have a chance to look carefully at the images formed by right angle mirrors, then you will notice that right angle mirrors produce three images. Interestingle, a single mirror produces a single image; another single mirror produces a second image; but when you put the two single mirrors toghether at right angles, there are three images.
A Pair of Parallel Mirrors
When the two mirrors are aligned at a 0-degree angle with each other (i.e., a parallel mirror system), there are an infinite number of images. Each image is the result of an image of an image, or an image of an image of an image or an image of an image of ...
Curved Mirror
we will turn our attention to the topoc of curved mirrors, and specificallly curved mirrors which have a spherical shape. Such mirrors are called spherical mirrors. Spherical mirrors can be thought of as a portion of a sphere which was sliced away and then silvered on one of the sides to form a reflecting surface. Concave mirrors were silvered on the inside of the sphere and convex mirrors were silvered on the outside of the sphere.
Beginning a study of sphereical mirrors demands that you first become acquainted with some terminology which will be periodically used..
Pricipal axis Center of Curvature Vertex
Focal Point Radius of Curvature Focal Length
It a concave mirror is thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror. This line is known as the principal axis. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter Aj in the diagram below. Thhe vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below. The distance form the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (represented by f). Since the focal point is the midppoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.
The Mirror Equation
To obtain the numerical information, it is necessary to use the Mirror Equation and the Magnification Equation. The mirror equation expressed the quantitative relationship between the object distance (do), the image distance di), and the focal length (f). The equation is stated as follows:
1 / f = 1 / do + 1 / di
The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). The magnification equation is stated as follows:
M = hi / ho = -di / do
These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.
Refraction
Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes form a fast medium to a slow medium bends the light ray toward the normal to th boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.
Refraction is responsible for image formation by lenses and the eye.
As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged: it is a characteristic of the source of the light and unaffected by medium changes.
Index of Refraction
The index of refraction is defined as the speed of light in vacuum divided by the speed of light in the medium.
The indices of refraction of some common substances are given below with a more complete description of the indices for optical glasses given elsewhere. the values given are approximate and do not account for the small variation of index with light wavelength which is called dispersion.
vacuum
1.000
Ethyl alcohol
1.362
Air
1.000277
Glycerine
1.473
Water
4 / 3
Ice
1.31
Carbon disulfide
1.63
Polystyrene
1.59
Methylene iodide
1.74
Crown glass
1.50 - 1.62
Diomond
2.417
Flint glass
1.57 - 1.75
Snell's Law
Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal.
Total Internal Reflection
When light is incideht upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection If. The exit angle will then approach 90° for some critical incident angle 0c , and for incident angles greater than the critical angle there will be total internal reflection.
The Critical Angle
Total internal reflection (TIR) is the phenomenon which involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met:
a light ray is in the more dense medium and approaching the less dense medium.
the angle of incidence for the light ray is greater then the so-called critical angle.
When the angle of incidence in water reaches a certain critical value, the refracted ray lies along the boundary, having an angle of refraction of 90-degrees. This angle of incidence is known as the critical angle; it is the largest angle of incidence for which refraction can still occur. For any angle of incidence greater than the critical angle, light will undergo total internal reflection.
So the citical angle is defined as the angle of incidence which provides an angle of refraction of 90- degrees
TIR and the Sparkle of Diamonds
Relatively speaking, the critical angle for the diamond-air boundary is an extremely small number. Of all the possible combinations of materials which could interface to form a boundary, the combination of diamond and air provides one of the largest difference in the index of refraction values. This means that there will be a very small nr/ni ratio and subsequently a small critical angle. This peculiarity about the diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small critical angle, light has the tendency to become "trapped" inside of a diamond once it enters. A light ray will typically undergo TIR several times before finally refracting out of the diamond. Because the diamond-air boundary has such a small critical angle (due to diamond's large index of refraction), most rays approach the diamond at angles of incidence greater than the critical angle. This gives diamond a tendency to sparkle. The effect can be enhanced by the cutting of a diamond gemstone with a strategically planned shape
mirage
A mirage is an optical phenomenon which creates the illusion of water and results from the refractiuon of light through a nonuniform medium. Mirages are most commonly observed on sunny days when driving down a roadway.
The Eye
The power of a lens is measured by opticians in a unit known as a diopter. A diopter is the reciprocal of the focal length.
diopters = 1/(focal length)
The maximum variation in the power of the eye is called the Power of Accommodation. If an eye has the ability to assume a focal length of 1.80 cm (56 diopters) to view objects many miles away as wen as the ability to assume a 1.68 cm focal length to view an object 0.25 meters away (60 diopters), then its Power of Accommodation would be measured as 4 diopters (60 diopters - 56 diopters).
The healthy eye of a young adult has a Power of Accommodation of approximately 4 diopters. As a person grows older, the Power of Accommodation typically decreases as a person becomes less able to view nearby objects. This failure to view nearby objects leads to the need for corrective lenses.
Farsightedness and its Correction
Farsightedness or hyperopia is the inability of the eye to focus on nearby objects. The farsighted eye has no diffulty viewing distant objects. But the ability to view nearby objects requires a different lens shape - a shape which the farsighted eye is unable to assume. Subsequently, the farsighted eye is unable to focus on nearby objects. The problem most frequently arieses during latter stages in life, as a result of the weakening of the ciliary muscles and /or the decreased flexibility of the lens. These two potential causes leads to the result that the lens of the eye can no longer assume the high curvature which is required to view nearby objects. The lens power to refreact light has diminished and the images of nearby objects are focused at a location behind the retine. On the retinal surface, where the light-detecting nerve cells are located, the image is not focused. These nerve cells thus detect a blurry image of nearby objects.
Thus, the farsighted eye is assisted by the use of a converging lens (double convex lens). This converging lens will refract light before it enters the eye and subsequently decreases the image distance. By beginning the refraction process prior to light reaching the eye, the image of nearby objects is once again focused upon the retinal surface.
Nearsightedness and its Correction
Nearsightedness or myopia is the inability of the eye to focus on distant objects. The nearsighted eye has no difficulty viewing nearby objects. But the ability to view distant objects requires that the light be refracted less. Nearsightedness will result if the light from distant objects is refracted more thann is necessary. The problem is most common as a youth, and is usually the result of a bulging cornea or an elongated eyeball. If the cornea bulges more than its customary corvature, then it tends to refract light more than usual. This tends to cause the images of distant objects to form at locations in ffront of the retina. If the eyeball is elongated in the horizontal direction, then the retina is placed at a further distance from the cornea-lens syste,. Subsequently the images of distant objects form in front of the retina. On the retinal surface, where the light-detecting nerve cells re located, the image is not focused. These nerve cells thus detect a blurry image of distant objects.
The cure for the nearsighted eye is to equip it with a diverging lens (double concave lenses). Since the nature of the problem of nearsightedness is that the light is focused in front of the retina, a diverging lens will serve to diverge light before it reaches the eye. This light will then be converged by the cornea and lens to produce an image on the retina.
Presbyopia
The power of accommodation of the eye usually decreases with ageing. For most people, the near point gradually recedes away. They find it difficult to see nearby objects comfortably and distinctly without corrective eye-glasses. This defect is called Presbyopia. It arises due to the gradual weakening of the ciliary muscles and diminishing flexility of the eye lens. Sometimes, a person may suffer from both myopia and hypermetropia. Such people often require bifocal lenses. A common type of bi-focal lenses consists of both concave and convex lenses. The upper portion consists of a concave lens. It facilitates distant vision. The lower part is a convex lens. It facilitates near vision. These days, it is possible to correct the refractive defects with contanct lenses or through surgical interventions.
Uses of convave mirrors
Concave mirrors ar commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light. They are often used as shaving mirrors to see a larger image of the face. The dentists use concave mirrors to see large images of the teeth of patients. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.
Use of convex mirrors
Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles. These mirrors are fitted on the sides of the vehicle, enabling the driver to see traffic behing him.her to facilitate safe driving. Convex mirrors are perferred because they always give an erect, though diminished, image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view much larger area than would be possible with a plane mirror.