18 Basic Optical Definitions

Naseer Iqbal

Learning Outcomes 

After studying this module, you shall be able to

• What are the essential features of light?
• How light gathering phenomena is important for a good telescopic observations.
• In what context the focal length determines the magnification of an optical system.
• Distinguish between the apparent field and a true field.
• Do we classify telescopes on the basis of fast and slow ones? If yes, how.
• Will the sky look always blue at a distance? Explain shortly.
• How seeing condition is important for good observations
• What are the necessary conditions for a good telescopic site?

1.  INTRODUCTION 

Light is part of the electromagnetic spectrum, which ranges from radio waves to gamma rays. Electromagnetic waves are fluctuations of electric and magnetic fields, which transport energy from one point to another. Visible light is not actually different from the other parts of the electromagnetic spectrum with the difference that the human eye can detect visible light very well. We can also discuss Electromagnetic radiation as a stream of mass less photons each travelling with wavelike properties at the speed of light. A photon is the fundamental (quantum) of energy which can be transported and it has been well accepted that light travelled in discrete quanta which reflects the originality of the Quantum Theory of light.

Detection of light coming from various objects in the universe is very important for probing the universe around us. As and when the light emits from a celestial object, it interacts with the component of the matter present there and as a result the originality of the incident radiation change and by using the physics of interaction of radiation with matter the properties of matter can be described. The description of this module will be incomplete unless and until the student is well versed with the details of “LIGHT”.

2.  Light its origin, Light rays and light waves.

Light is an electromagnetic radiation usually detected by the human eye. Electromagnetic spectrum occurs over a wide range of spectrum corresponding to their energy, wavelength and frequency figure (2.1). Within the overall spectrum the wavelengths visible to humans occupy a very narrow band, from about 700 nanometres (nm; billionths of a metre) for red light down to about 400 nm for violet light. The spectral regions adjacent to the visible band are often referred to as light also, infrared at the one end and ultraviolet at the other. The speed of light in a vacuum is a fundamental physical constant, the currently accepted value of which is exactly 299,792,458 metres per second, or about 186,282 miles per second.Light its origin, Light rays and light waves.

Light is a sense of sight and is regarded as a primary tool for perceiving the world and communicating within it. The sum emits electromagnetic spectrum of light, drives global weather patterns, and initiates the life-sustaining process of photosynthesis. The interactions of matter and energy have helped scientists to describe the shape, and the structure of the universe. Indeed, light provides a window on the universe, from cosmological to atomic scales. The whole information about the universe reaches Earth in the form of electromagnetic radiation. The astronomers while interpreting the received radiation on earth coming from trillions of stars describe the chemical composition of stars and Inter stellar medium ISM. The analyzing of the frequencies of light emitted and absorbed from atoms led the development of quantum mechanics. However, atomic and molecular spectroscopies continued to be primary tools for probing the structure of matter.

Figure 2.1 Electromagnetic Spectrum.

On the basis of the theory of classical electromagnetism, light is described as coupled electric and magnetic fields propagating through space as a traveling wave. However, this wave theory, developed in the mid-19th century, is not a sufficient one to explain the properties of light at very low intensities. Therefore a quantum theory is needed to explain the characteristics of light and to explain the interactions of light with atoms and molecules. In its simple form, light consisting of a discrete packets of energy, called photons whose energy is given by ?= ħ?. It is also said that, neither a classical wave model nor a classical particle model correctly describes light.   Light has a dual nature that is revealed only in quantum mechanics. In the middle of 20th century, a more comprehensive theory of light, known as quantum electrodynamics (QED), has been regarded by physicists as one of the appropriate theory for studying light as a whole.

2.1  Optical Laws 

Every science student should be able to know the following basic laws for studying the transmission of light

• Laws of Reflection and Refraction

How light reflects and refracts at smooth, plane interfaces. Figure 2.2 shows ordinary reflection of light at a plane surface, and Figure 2.3 shows refraction of light at two successive plane surfaces. In each instance, light is pictured simply in terms of straight lines, which we refer to as light rays.

Figure. 2.2 and 2.3  Light rays undergoing reflection and refraction at plane surfaces

After a study of how light reflects and refracts at plane surfaces, the procedure can be extended to smooth and curved surfaces, thereby having an interaction of light with mirrors and lenses which are the basic elements in different optical systems. A light ray is like an imaginary line directed along the path that the light follows. It is helpful to think of a light ray as a narrow pencil of light, very much like a narrow and a well-defined laser beam.

2.2  Light rays / Light waves. 

It is important to know the geometrical connection between light rays and light waves. Wave motion is visualized in terms of water waves (figure 2.4). The successive high points (crests) and low points (troughs) occur as a train of circular waves moving radially outward from the bobbing cork. Each of the circular waves represents a wave front. A wave front is therefore defined as a locus of points that connect identical wave displacements that is, identical positions above or below the normal surface of the quiet pond.

Figure 2. 4 : Waves / Rays of light.

In Figure 2. 4 b, circular wave fronts are shown with radial lines drawn perpendicular to them along several directions. Each of the rays describes the motion of a restricted part of the wave front along a particular direction. Hence, a ray is a line perpendicular to a series of successive wave fronts specifying the direction of energy flow in the wave. Figure- 2. 4 c shows plane wave fronts of light bent by a lens into circular (spherical in three dimensions) wave fronts that then converge onto a focal point F. The same diagram shows the light rays corresponding to these wave fronts, bent by the lens to pass through the same focal point F. This represents the connection between actual waves and the rays used to represent them. In the study of geometrical optics, we find it acceptable to represent the interaction of light waves with plane and spherical surfaces with mirrors and lenses in terms of light rays.

2.3 Reflection of light from Optical Surfaces 

It is important to understand the kind of a situation that erupts when light is incident on an interface between two transparent optical media like air and glass or between water and glass. There are four possibilities that can happen to the incident light.

• It can be partly or totally reflected at the interface.
• It can be scattered in random directions at the interface.
• It can be partly transmitted via refraction at the interface and enter the second medium.
• It can be partly absorbed in either medium.

In the study of geometrical optics smooth surfaces give rise to specular (regular, geometric) reflections (Figure- 2. 5a) and ignore ragged, uneven surfaces give rise to diffuse (irregular) reflections (Figure -2.5 b).

Figure 2.5 : (a) Specular reflection  (b) Diffuse reflection.

2.4 Light Gathering and Performance 

The strongest perception in the minds of people has been that the telescope automatically makes an object bigger and brings it closer to us. We should remember that the first thing Galieleo did in 1609 was to increase the magnification of the Dutch spyglasses. Because of the increase in magnification the telescope eyepiece enhances the angle under which an object is viewed and thus there is an increase in its apparent angular diameter. Hence the image taken has a larger area of the eyes total field of view, while maintaining (more or less) its true appearance. Earlier observers have expressed the magnification as an increase in angular size. The telescope gathers more light energy in the form of photons than the eye, making them available to form a brighter, more detailed image on any detector. The larger the lens or mirror, the larger, brighter and more distinct the image can be made. The energy gathering defines the true function of the telescope in terms of its brightness and resolution.

2.5 Aperture and Focal length 

The diameter of the open area of an objective lens or primary mirror that receives incoming light represents its aperture. Every telescopes primary optic focuses light at a specific distance away from its optical center. This distance is called as focal length abbreviated as FL. For a lens objective, the center point is based on the averaged optical powers of its component lenses. For a mirror, the FL is measured from the central point of the reflecting surface. FL determines the magnification of a system.

The focal ratio is defined as the ratio between an optical systems focal length and its aperture ( FL: D). For a human eye the focal ration can be calculated.

2.6 Field 

Two types of field are taken into consideration in the telescopic view of observations. They are the true field and the apparent field. The apparent field of the eye piece expresses the angle of view subtended by the circular  view within  its field and is independent  of  the telescope. True field on the other hand represents the angular measure of the image from the portion of the 3600 circle. It has been found that Binoculars have true fields between 40-60. True fields are usually calculated by the ratio between the apparent field of the eye piece used and the magnification quantity. Standard eye pieces have apparent fields between 40 and 65 degrees.

For any telescope the correct figure drawn and the focal length of its main optical elements are the primary physical descriptors of any telescope. This is true for all the kinds of mirrors and lenses used in a telescope. If these two things are up to the mark be sure that the performance of the telescope will be good.

2.7 Fast and Slow Telescopes 

This is a very technical term that is used in Telescopes. We call a telescope with a low f/ ratio number as a fast telescope and a telescope with large f/ratio number as a slow telescope. It has been seen that a low f/ ratio photographic lens exposes film more quickly as compared to the large f/ratio. Telescope makers have found that when the ratio f/ ratio is 12 or higher telescopes are slow. Moderate telescopes have f/8 and the fast one have f/4 to f/5.

2.8 Magnification 

The ratio between the focal length of the optical system and that of the eye piece determines the magnification (?=  MFLo/FLe). High magnification is achieved by using eye pieces of very short focal lengths. Under perfect conditions of the telescope, the aperture of the objective and the quality of the optics define the useful magnification of the object. It may be noted that keeping in view that image can be magnified beyond  some threshold value is not possible at all.

3. The clear blue sky. 

Color, brightness and polarization are three important parameters that one should know while talking about the sky.

• Color: The sky contains all colors. Near the horizon it is nearly white, but it may be tinted one of several colors due to reflection from the ground.
• Brightness: It is faintest at the zenith and rapidly brightens near the horizon. The sky is also darker at higher elevations.
• Polarization: Light from the sky is polarized, varying between around 85% at 900from the sun to zero at other places.

Sunlight consists of light of every wavelength and polarization plane. The unpolarized light is very close to perfect white. As it reaches the earth it begins filtering through the atmosphere. Rayleigh theory of scattering says that the probability that a single photon of sun light will be scattered from its original direction by an air molecule is inversely proportional to the fourth power of the wave length. The shorter the wavelength (or blue) the light is, the greater its chances are of being scattered. Thus when we look in any part of the sky except directly toward the sun, we mostly see a blue portion of scattered sun light than a red one. This causes the sky to appear blue.

The brightness of the sky is determined by the number of molecules in the line of sight: more air molecules mean a brighter sky. From a high flying jet the sky is darker than it is seen from the ground. This is because there are fewer air molecules in the line of sight. In space or on the moon, there are no molecules and therefore no scattered light is there to brighten the sky. There the sky is black.

4.  Seeing Conditions 

Astronomer’s describe the sky’s atmospheric conditions by using a technical term “Seeing”. Atmosphere is never smooth but continues to be always in a state of continual motion which results due to changing temperatures, air currents, weather fronts and dust particles. These factors cause the star images to twinkle. Twinkling of stars considerably have “poor” seeing conditions. If the above factors are very less we have “good” seeing conditions. Poor seeing is most noticeable when observing planets and the moon, whereas deep sky objects such as nebulae and galaxies are less affected by poor seeing conditions. On deep sky objects, the most important factor is the transparency of the atmosphere (a measure of how dark the sky is on a given night-determined by clouds, dust, haze and light pollution). Seeing conditions and transparency vary widely from site to site, from season to season and from night to night.

Seeing is used to indicate the quality of the observing conditions at the time of observation: it is the first point of the observer to evaluate the effects of atmospheric turbulence and impurities on the results of the observing.

SUMMARY

In this module, you study

• Origin of light and its spectrum.
• Optical laws  like  law  of  reflection  and  refraction,  Reflection  of  light  from  optical surfaces.
• Light gathering phenomena of an optical
• How any optical system has a good performance? What are various parameters must to have a good performance of an optical system.
• Aperture and focal length and how they are related with each other.
• Field of an optical system. Its relevance in observations.
• Factors classifying the telescopes on the basis of its fast and slow working.
• Magnification of an optical system. Classification of telescopes on the basis of its Magnification.
• Colour of Sky
• Conditions of seeing for telescopic observations.

References

For More Details (onthis topic and other topics discussed in Text Module) See

1. Telescopes and Techniques C.R.Kitchin, Springer 1995.

2. Observational AstrophysicsR.C. Smith, CUP 1995

3. Observational Astronomy D.S. Birney, G Gonzalez and D Oesper, CUP 20062nd Ed ISBN 0-521-85370-2