Galaxies are huge, swirling entities that consist of hundreds of billions to even trillions of stars. Our solar system lies in one of the spiral arms of a galaxy that we refer to as Milky Way because we see it as the faint, elongated cloud that you can see across the night's sky from a dark place. But there are billions of these galaxies, many of them bigger than our own. One of these bigger galaxies can be found in the constellation of Canes Venatici, the hunting dogs, and listens to the denominator NGC4631. In more popular terms, this galaxy's known as the Whale Galaxy because of its fairly odd shape. We see this galaxy edge-on but unlike ordinary spiral galaxies that are more or less symmetrical either side of the nucleus, this one has a bulge towards one end. The reason for this are two minor galaxies that are pulling the stars and other matter in the Whale in one direction. One of these accompanying galaxies can be seen on the sketch just below the Whale itself: NGC4627, aka the Whale's pup. The other lies exactly behind the big bulge and cannot be observed with ordinary telescopes. The gravitational pull causes great starburst activity in the Whale's bulge, as you can tell by the many bright patches within it. The sketch below was observed at 285x and you can see a myriad of detail.
Now let's increase telescope power to 507x and see what happens. Obviously we can't see the entire galaxy in one and the same field of view anymore as we've zoomed in considerably. The image dims because the light the telescope captures is smeared out over a much larger surface. But will we be able to make out even more details? In this case the image at higher power didn't show me more. Every telescope has a limit, also depending on the brightness of the object, and in case of the Whale Galaxy I had the impression that I had surpassed that limit. A friend of mine commented that on the high-power sketch there were still more details to be seen, and perhaps there were also at the eyepiece. Another interesting thing to note is that these two observations were made a month apart, so the high-power sketch was observed with a fresh mind, not influenced by my other sketch. But the 285x view looked a lot more pleasing and I didn't have to peer as much to see all the details as I had to do in the dim 507x view.
Astronomers call this the "sweet spot" of a telescope. It coincides with an exit pupil somewhere between 1 and 2 millimetres, or in other words the image that comes out of the telescope's eyepiece has a diameter of 1 to 2 millimetres. Or again in other words, you'll find the sweet spot of your telescope with an eyepiece with a focal length that's one to two times the focal ratio of your telescope. If you have a telescope with a focal ratio of f/5, then usually the best power to brightness ratio can be found with an eyepiece from 5 to 10mm. But as I said, this also depends on the kind of object. Small but very bright objects, such as planets or planetary nebulae, easily accept much higher powers, whereas very dim and large objects need much lower.