Quick optics 101

Here's a quick fun thing to do with a telescope on a rainy day.

Try this:
- point your telescope at something bright
- remove the eyepiece and place a piece of cardboard where it should be. Move the cardboard back and forth and you'll resolve an image!

Scroll over to 30 seconds or so to see the end result.

How does it work? We know from simple optics that if you have an image a distance d0 away, that another object will appear d1 away:

where f is the focal length of your telescope. Here is a schematic of the setup. The object is labeled "O" and the image "I".

Analyzing my setup, we see that d0 = 2.5m, and f is 700mm. This means with some algebra that we should expect an image at d1 = 1.03 m.

The object is at S1 and the image at S2+S3

What happens with images from the sky?

Images from the sky are actually located so far away that d0 is very large, and as a consequence 1/d0 goes away. This means then that:
1/d1 = 1/f

So if you did the same thing with the moon, you could use it to find the focal length of your mirror!