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# Refracting telescope.

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Introduction

#### 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 where is the focal length of the objective lens and is 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 . Thus, the angular magnification of the telescope is

Where is the focal length of the eyepiece and that of the objective? Note that the dependence of on and is different; here it is desirable for to 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.

Middle

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

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 () to that in a different medium is called the index of refraction and is usually labelled . For air, is close enough. For water, . For many types of glass, or 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:

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 is the position of the image, and is the position of the source. Is the magnification, the radius of curvature?

Magnification

## 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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