Operation of a microscope and image reconstruction I have a question about the operation of the optical microscope. With reference to the image:

from what I know, the image of the object is formed the first time where the red arrow is, why then is the microscope so long and inserts another lens higher up before the eye? Wouldn't it be enough to put the eye where I drew it? A little bit higher than the image? Why do we need the so-called eyepiece lens?
 A: It is true that a (finite conjugate) objective creates a magnified conjugate image inside the body tube of a microscope. To view this image directly an observer would have to align this image plane exactly on the conjugate plane of their retina projected by the eye's lens. For the image to remain focused you would have to stabilize your head to within the axial resolution x magnification (in the ballpark of 100um). You would have to do the same laterally which would be even more sensitive and impossible to do without clamping your had in a vice.
Thanks to the eyepiece, you only need to align the exit pupil of the compound microscope and the entrance pupil of the eye. In this case pupil really referrers to the image of the limiting aperture of each optical system. Since rays at the microscope pupil are parallel, it is quite insensitive to misalignment with respect to your eye.
An even more important reason is that the objective lens projects a real (inverted) image inside the body tube. If you were to observe this it would appear that the specimen is right in your face and you would have to focus your eyes very closely. The eyepiece, on the other hand, creates a virtual image of the real image. This is still inverted but appears to be rather far away from you so you don't strain your eyes.
A: It is very difficult to design a single lens with low distortion and high magnification; a compound lens to achieve the same is easier to do. Also as a practical matter, just imagine how sensitive to optimum position would a single lens of very large magnification would be considering any movement of your eye viewing the focal plane directly and to the distance of the lens to the object itself.
A: The magnification of a microscope is the product of the objective magnification times the eyepiece magnification. For example, a 4X objective matched with a 10X eyepiece gives a total magnification of 40X. So the eyepiece is an important component.
Additionally, the eyepiece provides a virtual image at some distance away, which for most people is a more comfortable location than right up against the intermediate image.
