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Refracting telescope.

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Introduction

5th January 2003

Refracting telescope

The telescope is also a compound lens system. In this case, we want to see objects, which are very far away, so one of the lenses will necessarily have a very large focal length. This contrasts with the microscope, which has a short focal length for the objective lens in order to see something very close. For the telescope, the intermediate image produced by the objective lens has a size image00.pngwhere image01.pngis the focal length of the objective lens and image11.pngis the angular size of the source. The eyepiece then acts the same as for the microscope; it takes the intermediate image as its object and magnifies it to a final angular size image19.png. Thus, the angular magnification of the telescope is


image20.png

Where image21.pngis the focal length of the eyepiece and image01.pngthat of the objective? Note that the dependence of image22.pngon image01.pngand image21.pngis different; here it is desirable for image01.pngto be as large as possible.

Aberrations

Briefly, there are two kinds of aberrations: monochromatic and chromatic. Monochromatic aberrations occur equally to light of all wavelengths.

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Middle

image02.png

Figure: Light refraction at a water-air interface. Snell's law in this case is image03.png.

The reason things happen differently in water as opposed to a vacuum is that light travels at a different speed. Light travels fastest in a vacuum. The ratio of the speed of light in a vacuum (image04.png) to that in a different medium is called the index of refraction and is usually labelled image05.png. For air, image06.pngis close enough. For water, image07.png. For many types of glass, image08.pngor so. The largest values are greater than 2.0.

We will see shortly how the hypothesis that light always picks the shortest route (time wise) between two points leads naturally to the law of refraction (Snell's law), which I state here:

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Conclusion

Upright or inverted: Real images are always inverted. Virtual images are always upright.

Magnification: The size of the image relative to the size of the object that created it.

Position: Where is the image (or where does it appear to be)?

To determine these characteristics, we follow a simple set of rules:

(a)

Take 2 different rays, both coming from the same point on the object.

(b)

See if they converge or diverge.

(c)

Take a third ray to verify the image.

(d)

Use ``simple" rays.

Important formulas

I end this lecture by reminding you of some important formulas for mirrors. Remember that image14.pngis the position of the image, and image15.pngis the position of the source. image16.pngIs the magnification, image17.pngthe radius of curvature?



Magnification

image18.png

Angular magnification

The magnification of an optical instrument is given by the angular magnification of the lens combination. Angular magnification is the ratio of the angular size of the image to that of the source. The angular size of something is its actual size divided by its distance from your eye. For example, the moon's angular size is about one degree.

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