What is the difference between chromatic aberration and a prism spectrograph

The Nicol prism Figure 10 takes advantage of this phenomenon. The e-rays emerge, linearly polarized and slightly shifted in path. A Wollaston prism Figure 11 is similar in effect but does not involve internal reflection of the o-rays. A Glan—Taylor prism Figure 12 is a common polarizing prism that separates the e-ray from the incoming beam.

It is composed of two right triangles of calcite or other birefringent material. The optical axis of the birefringent material is collinear with the polarization of the e-ray, and the two prisms are separated by a small space. In this prism, only the extraordinary ray is transmitted, while all of the ordinary ray and only some of the extraordinary ray is internally reflected.

A Glan—Foucault prism is similar, except that in this case, the optical axis of the calcite is perpendicular to that of the Glan—Taylor prism.

Finally, the Glan—Thomson prism is the same as a Glan—Foucault prism, except that the two right-angle prisms are glued together. This prism works the same way as the Glan—Foucault prism, but it has a lower limit of light input due to the potential for damage of the glue by the incoming light. David W. Ball is a professor of chemistry at Cleveland State University in Ohio.

With the appearance of this column, he is also a published poet. He can be reached at d. Paul R. Thanks for your four-part series on introductory quantum mechanics.

I even reviewed matrix algebra to verify that the multiplication of the 2 x 2 matrices as you showed is not commutative. September 1, Spectroscopy , Spectroscopy, Volume 23, Issue 9. Ball Dispersing Prisms As early as the 13th century, six-sided crystals of natural quartz were used to generate rainbows 2. Figure 1 Note in Figure 1 that the higher-energy blue light is refracted more than the lower-energy red light, implying that the index of refraction for blue light is higher than the index of refraction of red light — such is the general trend for most transparent materials.

Figure 2. Figure 3 A Dove prism Figure 4 is a piece of a right triangle prism with the right angle cut off parallel to the hypotenuse. Figure 4 A Porro prism takes advantage of two internal reflections to reverse the direction of incoming light Figure 5.

Figure 5 A rhomboid prism Figure 6 changes the position of the incoming light but not the direction or orientation of the image. Figure 6 Some prisms change the direction of light, but do so because they have silvered faces and not because of internal reflection. Figure 7 All of the prism examples so far have been single pieces, although some prisms like the Abbe prism can be constructed by cementing multiple triangular prisms together.

Figure 8 Polarization Effects Some solid, transparent crystals are birefringent — they have two different indices of refraction depending on the crystal axis that the light is passing through. Figure 9 The Nicol prism Figure 10 takes advantage of this phenomenon.

Figure 10 A Glan—Taylor prism Figure 12 is a common polarizing prism that separates the e-ray from the incoming beam. Figure 11 Figure 12 David W. References 1 E. Hecht, Optics , 4th ed. Addison-Wesley, New York, Why is chromatic aberration more evident from some positions of the aperture?

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Get the Answers App. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Answers. The light is therefore reflected back towards the centre of the primary mirror, where it passes through a hole on the optical axis and then onto an eyepiece.

This has the effect of extending the path of the reflected light before it is brought to a focus at F ext. The effective focal length of the system of two mirrors is the focal length of a single mirror having the same diameter as the objective and giving a cone of light converging at the focus at the same angle as the two-mirror system.

It is the effective focal length of the optical system which determines the size of the image, and in a Cassegrain telescope the effective focal length can be many times that of a Newtonian telescope of the same length. Both Newtonian and Cassegrain telescopes may be constructed using either paraboloidal objective mirrors or using spherical objective mirrors with Schmidt correcting plates. If a telescope is to be used with a photographic or electronic detector, instead of the eye, then we must allow a real image to fall onto the light-sensitive surface of the detector.

In this case there is no point in using the telescope with an eyepiece, since that produces a virtual image located at infinity. Remember, when you are actually looking through a telescope, the very final image is that produced by the lens of your eye.

This image falls onto your retina and is therefore a real image. However, the final image produced by the telescope , with the eyepiece in place, is a virtual image, located at infinity. The simplest solution is to remove the eyepiece entirely and place the detector in the focal plane of the mirror system i.

This also has the advantage of removing any aberrations introduced by the eyepiece lens. Alternatively, the secondary mirror may also be removed, and the detector may be placed directly at the prime focus of the main mirror i. This has the additional advantage of removing one more optical component, and with it the inherent aberrations and absorption losses that it contributes.

Figure 10 a shows a photograph of a modern optical reflecting telescope made to a Cassegrain design with an 8 m diameter parabolic primary mirror. Figure 10 b shows a much smaller Schmidt—Cassegrain telescope, of a type you may use as a student.

In comparison with refracting telescopes, the reflectors start with the important advantage of zero chromatic aberration. But they also score heavily on some aspects of practical construction and technology. For very large diameters 10 m or more it is much easier to produce mirrors than lenses because the glass does not have to be perfectly transparent or optically homogeneous and a mirror can be fully supported on the rear surface.

The grinding and polishing is carried out on only one surface, which is finally covered by a thin reflecting layer, usually of aluminium. On the debit side, there is greater loss of optical intensity in reflectors than in refractors, because the reflecting surfaces are never per cent reflective and may have appreciable absorption. Aluminised surfaces also deteriorate rather quickly and have to be renewed every few years.

On the other hand, a perfectly polished lens remains serviceable for many years. Having looked at the different designs of optical telescopes and the various problems inherent in their construction, we now turn to the ways in which their performance may be characterised.

We consider five main performance characteristics, each of which may be applied to both refracting telescopes and reflecting telescopes. One of the key benefits of using a telescope is that it enables fainter objects to be detected than with the naked eye alone. The light-gathering power of a simple telescope used with an eyepiece is defined as.

This is proportional to the light-gathering area of the objective lens or mirror of the telescope. Hence for the three telescopes we have, converting all diameters to mm :. Clearly, the larger the aperture the more light is collected and focused into the image, and therefore fainter stars can be detected.

The field-of-view of a telescope is the angular area of sky that is visible through an eyepiece or can be recorded on a detector, expressed in terms of an angular diameter. When a telescope is used with an eyepiece, the angular field-of-view is equal to the diameter of the field stop i.

In symbols:. What is the field-of-view, in arcminutes, of a telescope whose focal length is mm when used with an eyepiece with a field-stop diameter of Converting to degrees, this is. When a telescope is used with a detector in place of an eyepiece, the determining factor here is the linear size of the detector itself, rather than the field-stop diameter. A focal length longer than this would reduce the field-of-view. Scales such as these indicate how the size of the reproduction compares to the real thing.

Image scales are no less important in astronomy, though they are usually stated in a different form, as we now explain. Imagine for a moment that you have the use of a telescope that allows you to observe Saturn and its ring system.

It must be very highly magnified to show so much detail, mustn't it? Well, consider the size of the image. It is in fact greatly de magnified, by such a large factor that the image of the km diameter planet fits on the light-sensitive surface of your eye only a few millimetres across. The same would be true if you recorded the image on photographic film or with a digital camera. Yet you know you can see more detail than with the naked eye.

This simple example emphasises that the important magnification in much astronomical imaging is not the linear magnification described above for terrestrial maps, but rather the angular magnification.

The angular magnification indicates by what factor the angular dimension e. So if you were to observe Saturn through a telescope, you would be benefiting from a high angular magnification which makes the image appear larger even though it is squeezed into the tiny space of your eyeball. The angular magnification M of an astronomical telescope, used visually, is defined as the angle subtended by the image of an object seen through a telescope, divided by the angle subtended by the same object without the aid of a telescope.

By geometry, this can be shown to be equivalent to. The larger the focal length of the primary mirror, the greater will be the angular magnification of the telescope. Notice that the angular magnification and field-of-view of a telescope both depend on the focal length of the objective lens or mirror. However, increasing f o will increase the angular magnification but decrease the field-of-view, and vice versa. The nearest equivalent definition to angular magnification that is applicable to telescopes used for imaging onto a detector is the image scale sometimes called the plate scale.

Because of the importance of angular measures, the image scale quoted by astronomers indicates how a given angular measure on the sky corresponds to a given physical dimension in an image. The most common convention is to state how many arcseconds on the sky corresponds to 1 mm in the image. Fortunately, it is very easy to calculate the image scale for any imaging system, as it depends on only one quantity: the focal length f o of the imaging system. The image scale I in arcseconds per millimetre is given by.

Note that as the image on the detector becomes larger , the numerical value of I becomes smaller. A certain telescope has an objective with an effective focal length of What is the image scale in the image plane? The image of a point-like source of light such as a distant star obtained using a telescope will never be a purely point-like image.

Even in the absence of aberrations and atmospheric turbulence to distort the image, the image of a point-like object will be extended due to diffraction of light by the telescope aperture.

The bigger the aperture, the smaller is the effect, but it is still present nonetheless. The intensity of the image of a point-like object will take the form shown in Figure 11 a.

The structure shown here is referred to as the point spread function PSF of the telescope. Lens or mirror aberrations and atmospheric turbulence will each cause the width of the PSF to broaden, and may cause its shape to become distorted too.

However, in the ideal case when neither aberrations nor turbulence is present, the telescope is said to be diffraction-limited , and its PSF has the form shown. The width of the PSF, in this idealised case, is inversely proportional to the aperture diameter of the telescope. Using the idea of the diffraction-limited PSF, we can also define the theoretical limit of angular resolution for an astronomical telescope.

This is the minimum angular separation at which two equally bright stars would just be distinguished by an astronomical telescope of aperture D o assuming aberration-free lenses or mirrors and perfect viewing conditions.

As shown in Figure 12 b, at a certain separation, the first minimum of the PSF of one star will fall on the peak of the PSF of the other star.

At this separation, the two stars are conventionally regarded as being just resolved. The angular separation corresponding to the situation in Figure 12 b is given by. As noted above, the limit of angular resolution arises due to diffraction of light by the telescope aperture and represents a fundamental limit beyond which it is impossible to improve.

A certain ground-based reflecting telescope contains aberration-free optical components and has a primary mirror aperture mm in diameter. If two stars of equal brightness are observed through a red filter that transmits only light of wavelength nm, what is the theoretical minimum angular separation in arcseconds at which these two stars could be just resolved? In practice, two stars this close together are unlikely to be resolved using a conventional ground-based telescope, whatever its aperture diameter, because of the degradation of angular resolution imposed by turbulence in the atmosphere.

In effect therefore, atmospheric turbulence broadens the PSF of the telescope. In fact, in most ground-based observatory telescopes, the dominant contribution to the size of the PSF is generally from atmospheric turbulence rather than imperfections in the telescope optics or the theoretical limit to angular resolution imposed by diffraction.

Hence, the diameter of the actual point spread function is a common way of quantifying the astronomical seeing. At the very best, the seeing from a good astronomical site is around 0. If it's never possible to achieve a diffraction-limited point spread function, because of atmospheric turbulence, what's the point of building a ground-based optical telescope with a mirror diameter of 5 m or more?

A 5 m mirror will have a theoretical limit of angular resolution of about 0. However, the advantage of the 5 m mirror is that its light-gathering power is times greater than that of a mirror of 10 times smaller diameter. So much fainter astronomical objects may be detected. Despite what has just been said, there is a technique now available at some professional observatories for reducing the effects of poor seeing, and attaining close to the theoretical limit of angular resolution.

The technique of adaptive optics refers to a process whereby corrections to the shape of the primary or secondary mirror are made on a rapid timescale hundredths of a second to adjust for the image distortions that arise due to atmospheric turbulence.

A relatively bright reference star is included within the field-of-view, or an artificial laser guide star is produced by directing a laser into the atmosphere. The adaptive optics system then rapidly adjusts the mirror under software control in order to make the size of the PSF of the reference star as small as possible. By correcting the reference star in this way, all other objects in the field-of-view have their PSFs similarly corrected, and an angular resolution close to the theoretical limit may be obtained.

A telescope with the largest light-gathering power, best point spread function and optimum image scale and field-of-view is of little use unless it is mounted in an appropriate way for tracking astronomical objects across the night sky. It is essential that a telescope can be pointed accurately at a particular position in the sky and made to track a given position as the Earth rotates on its axis. Broadly speaking there are two main types of mounting for astronomical telescopes, known as alt-azimuth and equatorial.

An alt-azimuth mounting alt-az for short is the simplest to construct. It allows motion of the telescope in two directions, namely the altitude or vertical direction and the azimuth or horizontal direction Figure 13 a. Although simple and relatively cheap to construct, it has the drawback that to accurately track an astronomical object such as a star or galaxy requires the telescope to be driven in both axes simultaneously at varying speeds. Given the widespread availability of computer software to do the job this is not a problem in practice.

However, another limitation is that the image will rotate as the telescope tracks, and therefore the detector must also be counter-rotated during any exposure in order to produce an un-trailed image.

The other type of mounting is known as an equatorial mounting. In this case, one axis of the telescope is aligned parallel to the rotation axis of the Earth the so called polar axis , and the other axis the so called declination axis is at right angles to this Figure 13 b. This has the advantage that once the telescope is pointed at a particular star or galaxy, then tracking of the object as the Earth rotates is achieved simply by moving the telescope at a constant speed around the polar axis only.

For a given location on the Earth, what determines the angle between the polar axis of an equatorially mounted telescope and the horizontal? An equatorial mounting is relatively expensive to construct, but it is much simpler to drive and point a telescope with such a mounting, particularly without computer assistance, and the field does not rotate during the course of an exposure.

At what speed must a telescope be moved around the polar axis of an equatorial mounting in order to counteract the effect of the Earth's rotation? Converging lenses or mirrors cause parallel beams of light to be brought to a focus at the focal point , situated at a distance of one focal length beyond the lens or one focal length in front of the mirror. Diverging lenses or mirrors cause parallel beams of light to diverge as if emanating from the focal point of the lens or mirror.

Light paths are reversible, so a converging lens or mirror may also act as a collimator and produce a parallel beam of light. The simplest astronomical telescopes are refracting telescopes comprising either one converging lens and one diverging lens Galilean telescope , or two converging lenses Keplerian telescope.

The effectiveness of refracting telescopes is limited by the problems involved in constructing large lenses, and their spherical and chromatic aberrations which are, to some extent, unavoidable. Reflecting telescopes, such as the Newtonian and Cassegrain designs, make use of a curved concave objective primary mirror to focus the incoming light. Reflecting telescopes are free from chromatic aberrations. Spherical aberrations can also be greatly reduced by using a paraboloidal mirror or a Schmidt correcting plate.

Large-diameter reflecting telescopes are easier to construct than similar sized refractors. Also, by using the Cassegrain design, a long focal length and hence high angular magnification can be contained in a relatively short instrument. When reflecting telescopes are used with photographic or electronic detectors, the eyepiece is removed, and sometimes so also is the secondary mirror. This removes the aberrations and absorption losses that are due to these components and allows a real image to fall directly onto the light-sensitive surface of the detector.

The main parameters of an optical telescope are its light-gathering power, its field-of-view, its angular magnification or image scale and its limit of angular resolution. The angular size of the point spread function of a telescope can be used to quantify the astronomical seeing. The technique of adaptive optics can compensate for the effects of atmospheric turbulence and produce images whose PSFs are close to being diffraction-limited.

A telescope may have an alt-azimuth or equatorial mounting. The former is less complex to construct, but with the latter it is simpler to point and drive a telescope. In practice, of course, for ground-based telescopes, atmospheric seeing is usually the limiting factor. What is the aperture of a diffraction-limited telescope at a wavelength of nm which would have a resolving power equivalent to this seeing? The main reason that very large ground-based telescopes are built is to increase the available light-gathering power.

List the important advantages and disadvantages of reflecting telescopes compared to refracting telescopes. Its shape is calculated so as to introduce some differential refraction to various parts of the incoming wavefront, in such a way as to compensate for the spherical aberration of the main mirror.

The result is good resolution over a significantly wider field-of-view. The remainder of the telescope is the same as the normal Cassegrain type. The overall design is shown in Figure The f-number, 10, is the focal length divided by the diameter, i.

Telescopes may simply be used to collect the light from an astronomical object in order to measure its position, brightness or spatial distribution. However, it is often far more instructive to examine the spectrum of light from an object such as a star or galaxy, namely the distribution of light intensity as a function of wavelength.

The spectrum of a light source may be revealed in several ways, all of which involve making light of different wavelengths travel in different directions, a process which we term dispersion. There are two principal ways of dispersing light: using either a prism or a grating.

The simplest way to disperse light is to use a prism. When light enters a prism, it is no longer travelling in a vacuum, and its speed decreases. If the incident wavefront is travelling at an angle to the surface of the prism, which is easy to arrange because of its angled faces, then the propagation of the part of the wavefront in the prism is retarded, thus bending the wavefront and changing its direction of propagation through the prism Figure This phenomenon is referred to as refraction.

The speed of light in most materials depends on frequency, so the change in direction also depends on frequency, and hence different colours become separated.

Figure 16 illustrates the situation when a beam of white light i. The white light is dispersed at the air-glass boundary and, because of the shape of the prism, the different colours undergo further dispersion at the glass-air boundary as they leave the prism. When light, or indeed any type of wave, passes through a narrow aperture, it will spread out on the other side.

This is the phenomenon of diffraction. For example Figure 17 shows the diffraction of water waves in a device called a ripple tank. The extent to which waves are diffracted depends on the size of the aperture relative to the wavelength of the waves. If the aperture is very large compared to the wavelength, then the diffraction effect is rather insignificant.

So although sound waves may be diffracted by a doorway, light waves are not appreciably diffracted by doorways because the wavelength of visible light about to nm is very small in comparison to the width of the doorway.

But light is diffracted, and provided the slit is narrow enough, the diffraction will become apparent. The phenomenon of diffraction allows us to appreciate the effect of an aperture on the propagation of waves, however it says nothing about what will happen when waves from different sources or from different parts of the same source meet.

For this, the principle of superposition must be used. The principle of superposition states that if two or more waves meet at a point in space, then the net disturbance at that point is given by the sum of the disturbances created by each of the waves individually.

For electromagnetic radiation the disturbance in question can be thought of as variations in electric and magnetic fields. The effect of the superposition of two or more waves is called interference. To begin with, we consider the diffraction of monochromatic light by a pair of closely spaced, narrow slits as shown in Figure Plane waves of constant wavelength from a single, distant, source are diffracted at each of two slits, S 1 and S 2.

Because the waves are from the same original source they are in phase with each other at the slits. At any position beyond the slits, the waves diffracted by S 1 and S 2 can be combined using the principle of superposition. In the case of light waves, the resulting illumination takes the form of a series of light and dark regions called interference fringes and the overall pattern of fringes is often referred to as a diffraction pattern.