I respect A.J's insight a lot, but I don't agree that a brewer's microscope has to cost $1500.
What we are using the microscpope would be:
- cell counting
- looking at yeast in general
- identifying haze
- possibly identifying contaminants
The latter is tricky since once there are enough bacteria so you see them in a sample your beer should have a significant off flavor already.
A few years back I bought a up to 1000x (100X oil immersion objective and 10x eyepiece) monocular student microscope new for $160 from Cynmar and I'm happy with it.
at 1000x yeast look like this:
Sure, the pic may have been better with a $1500 scope, but that doesn't detract from its usefulness.
These days I generally count yeast from cell-phone photos like this
. The image is blurred on the edges b/c I just held the phone camera to the eyepiece. This is not how I see the cells when I look through the microscope.
I do cell counts with ImageJ: