Can you use a microscope without an eyepiece?
Yes, you can. I have a microscope where the data can be transferred to a screen on a computer instead of going to the eyepiece. This microscope has both an eyepiece and the option to redirect the image to a screen. However, I also have a microscope with a screen only. So, I suppose you can have a microscope without an eyepiece.
I have never come across a microscope that has neither an eyepiece nor a camera but I don't know whether it's possible or not.
A microscope composed of a single lens is called a simple microscope. In fact you can use an objective or just the eyepiece, as a magnifying glass. Antonie van Leeuwenhoek's microscope's were simple microscopes.
In contrast, compound microscopes (by far the most common type nowadays) are composed of two or more lenses. I would argue that their benefits compared to simple microscopes include:
- Multiplicative magnification arising from the combination of lenses.
- Ease with which the objectives can be interchanged independently of the eyepiece offering different magnifications.
- Easier to achieve an ergonomic design.
- Advanced illumination setups, such as phase contrast.
- Cheaper to provide stereoscopic vision and achieve parfocallity with two low-magnification lenses that are able to be focused independently than having two high-magnification lenses.
- Some eyepieces additionally correct for aberrations.