Last night I went out to the desert to take a picture of the Crab Nebula. My telescope is not really up to the task, but I've always wanted to do it anyway.
But I have no pictures of the Crab for you. I tried it two ways: with my narrowband filter and without. The filtered image was far superior. However, it was also out of focus due to some bad frames. But even with the bad frames removed the focus was still bad. Maybe I need to focus with the filter in, although I can't figure out why that would change things. Or maybe the focus was OK and, as suspected, the Crab is just too small for my telescope to capture well.
Anyway, I'll try again next month. In the meantime, here is the Pacman Nebula, aka NGC 281, which gets its name from the fact that it sorta looks like a Pacman muncher.
It does not look like Pacman.
But if you rotate it 90 degrees counter-clockwise it looks like a guy with a huge mustache and a lot of hair.
If you focused with the filter out, and then inserted the filter and kept the same focus, the filter will definitely move the focal point of the objective lens in the direction away from the objective.
A parallel plate of glass (a filter) in a converging beam will displace the focus by an amount equal to (plate thickness) * (n-1)/n, where n is the index of refraction of the glass.
The filter is probably BK-7 or equivalent, for which n is about 1.5, so if the filter is 2 mm thick, the focus will move out by (0.5/1.5)*2mm, or about .66 mm. Enough to notice.
"Maybe I need to focus with the filter in, although I can't figure out why that would change things. "
Because glass is not air. If you look on the documentation for any quality filter, it will tell you how far that filter moves the focus point i.e. how much it changes the effective optical path. Refraction, you know. See Adam Strange.