A Quick Note on Telescopes

What are the two primary purposes of using a telescope instead of the naked eye?

I'm not really sure I can boil this question down into two specific primary purposes--the way I see it, there are three things that make telescopes (particularly modern telescopes) so remarkably useful, all of which boil down to one simple statement: a telescope, whether you're using one you bought from Toys "R" Us (I looked that one up--it is actually double quotation marks around the R) or Keck, lets you see more. The most obvious way is that having a really big lens or mirror gathering light and focusing it to a point is a vast improvement over the light-gathering ability of a pupil just a few millimeters across.

Related to that is exposure time, or how long your detector gathers light for before it turns it into an image. For the eye, it's incredibly short, which makes sense--if the eye had a long exposure time, all you would ever see would be disjointed, incredibly blurry images. But that's not to your advantage when you're trying to look at a distant astronomical object. Using a CCD (or if you're feeling old-school, a photographic plate) means that you can point a telescope at an object and, as long as it tracks it across the sky, gathering photons the entire time and assembling them into a single highly detailed image.

The eye is also limited by wavelength, and a telescope can get around that as well. Our eye does see pretty well, but only in the visual band of wavelengths (from around 400-700 nm). But you can build a telescope to examine in any wavelength you want. Many telescopes are designed to observe across a range of wavelengths (Hubble, for instance, observes from the UV through the visible into the near-IR). Others like the Chandra X-Ray Observatory or Arecibo can't observe in the visual spectrum at all.

Last, but certainly not least, we have angular resolution. The smallest angle that a detector can resolve is $\lambda / D$, where $\lambda$ is the wavelength of the light being observed, and $D$ is the diameter of the detector, so a much larger detector allows you to resolve a much smaller angle on the sky. In most cases, though, this is limited by interference by the Earth's atmosphere--except on timescales shorter than about 10 microseconds or angles greater than about one arcsecond, angular resolution stops improving in ground-based telescopes above $D = 10$cm. Fortunately, there are a few ways around this.

In "speckle" or "lucky" imagine, a telescope takes an enormous number images with exposures under 10 msec and combines them into a single image. However, this is unhelpful for very dim objects that are undetectable in under 10 msc, and thus only works for bright point sources. Thus, a more common solution is adaptive optics, which rapidly adjust the position of a reflecting telescope's secondary mirror to account for atmospheric interference. The downside of this is that it's extremely difficult, particularly in the visible spectrum--at the moment there's only one telescope in the world using adaptive optics in anything other than the near-infrared. It also requires a bright point source for calibration. This, it would seem, would mean that attempting to image a distant galaxy without stars in the foreground would be futile. Except here again, technology has filled in where nature is lacking--without a point source to calibrate by, observatories substitute a laser which excites sodium in the uppermost reaches of the Earth's atmosphere. These sodium molecules then give off light which propagates back down through the atmosphere and is subject to the same interference as sources in outer space. Plus, it means we get photos like this one, of the Keck telescopes:

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Of course, if all of that sounds like too much trouble, and you have a few billion dollars to blow, there is one other solution...

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