The study of optics can be divided into three parts: physical, geometric , and physiologic . Physical optics is primarily concerned with the nature and properties of light itself. Geometric optics is that branch of optics in which the laws of geometry can be used to design lenses that include spectacles, optical instruments, telescopes, microscopes, cameras, and so forth. Physiologic optics deals with the mechanism of vision and the physiology and psychology of seeing. We deal here primarily with physical and geometric optics.
Physical optics
What is light?
Our ancestors pondered and theorized about the nature of light. One theory proposed that light was wavelike and spread like ripples across a still pond ( Fig. 3.1 ). Another theory held that light was a flight of particles similar to the shooting out of droplets of water from the nozzle of a hose ( Fig. 3.2 ). In more recent times scientists have believed that there is truth in both theories: that light can be transmitted both as particles and as waves.
How does light travel?
Light, which is basically that aspect of radiant energy to which the eye responds as a visual experience, is called luminous radiation . The light waves travel in a specific direction. The movement of these waves is in an up-and-down motion perpendicular to the direction in which they travel ( Fig. 3.3 ). These same light waves are capable of producing vision in human beings and lower animals by stimulating the very sensitive photoreceptors in the retina.
Nature of the world visible to humans
Human beings are continuously bombarded by electromagnetic energy, including waves from radio transmitters, infrared rays from heat lamps, and ultraviolet rays from the sun and quartz lamps, without receiving any visual sensation as a result of being in contact with these sources. It is only a portion of this electromagnetic spectrum that determines the visible world. The wavelengths of some of the waves of the electromagnetic spectrum are extremely short; for example, cosmic rays are only about 4 trillionths of a centimeter in length. Other wavelengths, such as those of radio waves, may be as long as 2 to 3 miles (3–5 km). The rays of wavelengths to which the eye responds lie in about the middle of this spectrum, namely, from 400 to 800 nm. Fig. 3.4 , an illustration of the electromagnetic spectrum, indicates the range of wavelengths for various parts of the spectrum.
Speed of light
Light travels at a speed of 186,000 miles per second (300,000 km/s). It is many times faster than sound, as is evident by the fact that we see a lightning flash much sooner than we hear the thunder that follows. Each wavelength is the distance from the crest of one wave to that of the next, whereas the frequency is the number of wavelengths passing a given point in 1 second. The product of these two quantities is equal to the speed of the electromagnetic radiation ( velocity is the speed in a particular direction).
The speed of light in air is greater than that in other transparent media. For example, the speed of light in ordinary glass is only about two-thirds of the speed in air. However, we designate the wavelength of light in terms of its speed in air.
How do we measure intensity of a light source?
Light intensity is traditionally measured in terms of footcandles , a standard dating from preelectricity times. The light from a single candle falling on a surface at a distance of 1 foot illuminates the surface with an intensity of 1 candle per square foot. This is the premetric unit of measurement of light. If we hold a candle near a book to read, we soon find that as we move the candle away from the book, there is a distance at which the illumination is insufficient to permit us to read. The illumination of light on a surface is inversely proportional to its distance from the light source ( Fig. 3.5 ). The luminance of an object depends on the light reflected, and the equivalent visual sensation is one of brightness. An illumination of 10 footcandles is sufficient for ordinary indoor tasks; 30 footcandles is adequate for sewing and reading, although we often choose a reading lamp that will give us as much as 50 footcandles ( Table 3.1 ).
| Venues and tasks | Minimum footcandle level |
|---|---|
| Auditoriums | 15 |
| Waiting rooms | 15 |
| Building corridors and stairways | 20 |
| Libraries | 70 |
| Art galleries | 30 |
| Reading rooms | 30 |
| Study desks | 70 |
| Store interiors | 30 |
| School chalkboards | 150 |
| Kitchen work surfaces | 50 |
| Prolonged sewing | 100 |
Because the original standard candle cannot be easily reproduced, it has been replaced by a group of carbon filament lamps operated at a carefully prescribed voltage and maintained in the vaults of the U.S. Bureau of Standards. In modern usage, the amount of illumination, or illuminance, is referred to in terms of lumens (the International System of Units [SI], commonly known as the metric system ) per foot rather than candles per foot.
Color
The dispersion of white light into its many component colors was first demonstrated by Sir Isaac Newton, who allowed a narrow beam of light to pass obliquely through a prism and then intercepted the transmitted light, which appeared as colored bands or as a spectrum on a screen. The colors he found were spread into definite bands that the normal eye identified as red, orange, yellow, green, blue, and violet. The sequence of hues was always found to be in the same order. Newton called these bands of color the spectrum and he called the spreading effect caused by the prism dispersion . He was the first to show that white light is really a mixture of all colors. We enjoy everyday examples of this phenomenon of light breaking up into its constituent colors. Rainbows, for example, are produced by the dispersion of light into its spectral parts by droplets of rain or mist in the air.
Each wavelength range has a particular color hue. Red, having the longest wavelength, is deviated least by a water droplet or a prism and therefore appears at one end of the spectrum. Violet, which has the shortest wavelength, appears at the other end of the spectrum ( Fig. 3.6 ).
Rays of light and the spectrum
A single ray of light is the path of a single corpuscle of light traveling through a tiny aperture through two successive screens.
A pencil of light is a group of rays that diverges from its point source. It might pass through the aperture of one screen but would not make it through the aperture of the other.
A beam of light is a group of pencils of light. A relatively large aperture is required to admit a beam.
Each filament in an electric bulb has a number of beams and pencils of light. These beams diverge and overlap one another. At close range, they strike an object and create overlapping shadows that are poorly defined. The further the light source, the more parallel are the beams of light. That is why shadows framed from the sun are sharper and more finely etched than those coming from an artificial light source.
Where rays of white light pass through cut glass, they frequently are broken down into lights of varying wavelengths. The longest wavelength is red, followed by orange, yellow, green, blue, and violet.
| Red | 650–750 nm |
| Orange | 592–650 nm |
| Yellow | 560–592 nm |
| Green | 500–560 nm |
| Blue | 446–500 nm |
| Violet | 400–446 nm |
The fragmentation of white light yields the visible spectrum. There are other wavelengths not visible to the eye, including ultraviolet, infrared, x-ray, radio, and electromagnetic waves.
White light is not regularly broken up unless it travels into and through a different medium, such as water droplets or glass. It is important to realize that the various wavelengths travel forward or outward at the same speed. Only their vertical vibrations differ in frequency. Thus the speed of violet light in air is the same as yellow, red, or green (i.e., 186,000 miles per second).
When white light enters the eye, all these light waves are moving at the same speed but with a different vibration. These waves fuse, giving the sensation of white even though they travel through the eye, which has a different index of refraction than air.
Bending of light
Most people will have observed that a straight pole placed in a clear pond no longer looks straight but appears to be bent at the surface of the water. Fish under the surface of the water appear to someone fishing to be at a different place from where they actually are ( Fig. 3.7 ). This phenomenon is caused by refraction of light.
If light travels in a straight line, how does one explain this apparent bending of light? Snell discovered the law behind this everyday phenomenon: it was explained by assuming (and this assumption was later proved correct by experiment) that light travels at different speeds in different media. We have stated that light travels in a vacuum at 186,000 miles per second. However, as it travels through other media, such as water or glass, it travels at a slower velocity. The rate at which light travels through water is 140,000 miles per second (~225,800 km/s).
Other media, such as glass and the chambers of the eye, also retard the velocity and alter the direction of light. The ratio of the speed of light in a vacuum to that in a given medium is called the index of refraction of that medium. This index, which is a comparison of the speed of light through a particular medium to its speed through air, can be expressed as follows:
For water this index is:
Thus the index of refraction of a substance determines the speed of light through it. The index of refraction of the common optical media can be expressed as follows:
Air = 1.00
Water = 1.33
Aqueous humor = 1.336
Cornea = 1.37
Lens cortex = 1.38
Lens nucleus = 1.40
Crown glass = 1.49
Polymethylmethacrylate (PMMA) plastic = 1.52
Flint glass = 1.65
How light can alter its direction
If rays of light pass from the air through another medium, such as a plate of glass, and pass perpendicularly to the glass, they will be slowed down somewhat but will emerge along the same line on which they entered the medium ( Fig. 3.8A ). If, however, these rays pass obliquely at any angle to the plate of glass, they will be bent a little at the surface. The oblique rays closest to the glass will enter the glass first, and these rays will be slowed down first on their pathway through the slower medium ( Fig. 3.8B ).
This is similar to the slowing-down effect when a line of soldiers marches at an angle toward a deep sandbar ( Fig. 3.9 ). The soldiers who first enter the sandbar will be slowed down first, whereas those at the extreme end will continue at their original speed until they reach the sandbar. This will result in a bend in the straight-line formation. This same effect occurs when a beam of light strikes a glass surface at an oblique angle.
Geometric optics
Terminology
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Divergence . Rays of light from any luminous point of light will spread out or diverge ( Fig. 3.10A ).
Fig. 3.10
(A) Divergence. (B) Convergence. (C) Parallel rays.
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Convergence . When a bundle of rays is brought together, the rays are said to converge ( Fig. 3.10B ).
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Parallel rays . Light rays are assumed to be parallel if they emanate from a distant light source, such as the sun ( Fig. 3.10C ).
A ray of light entering a medium is called the incident ray and the same ray emerging from the medium is called the emergent ray . The angle that the incident ray makes with the perpendicular surface of the medium is called the angle of incidence . The angle the ray makes within the medium by its change of direction is called the angle of refraction ( Fig. 3.11 ).
The relationship between these two angles and the index of refraction of the medium through which the ray of light passes is the basis of Snell’s law , a fundamental law in optics that governs the refraction of light by a transparent substance. Snell’s law states:
It is on this constant relationship of the angle of incidence, angle of refraction, and index of refraction of the medium that all lens design depends.
Dispersion
If a spectrum of light travels through a glass with parallel sides, then the deflection of light is such that the emerging rays are parallel to the direction of the original incident rays. The white light may enter a new medium, such as glass, be broken up into its spectral components, and then fuse on the way out into a white bundle of rays.
If a ray of light goes through a glass whose sides are not parallel, the white light will be broken up into its spectral components with the various wavelengths emerging in different directions. This effect, called dispersion , results in colored fringes found around anything viewed through prisms or unevenly cut glass. The dispersion value of different types of glass varies, depending on its index of refraction ( Fig. 3.12 ).
Color
White light is made up of beautiful colors. This easily can be seen when a narrow beam of white light is passed through clear plastic, which bends the white light at different angles. Sir Isaac Newton, a famous English scientist, made this discovery in 1666. When mist disperses white light it gives rise to the rainbow. Red, green, and blue are the primary colors. In dim light, more sensitive cells in the rods of the retina take over, which explains why we see mainly black and white as it gets darker.
Mirrors and reflection
One way of changing the direction of light is to allow light to rebound from a surface and thus be thrown in another direction. This rebounding of light is called reflection and certain laws govern its behavior. Any reflecting surface, such as glass, water, or metal, can reflect light. Because glass and water transmit light primarily, their reflection is secondary. Many other examples of reflecting surfaces are found in nature, such as a still pond or lake ( Fig. 3.13 ).
