In a microscope there are two major lenses, although some microscopes may have more. In use, students find the images they see are both inverted and enlarged.Their teachers tell them to keep both eyes open when they use a microscope. Physics will help us understand both the teacher's instructions and the nature of the images that are seen.
In practice, we place an object just outside the focal point of a convex lens. The real image formed by that first lens will be used as the object for the second lens, the one we look through directly.
In our diagram, the object is the small arrow and the focal points of the two lenses are shown with subscripts to denote which lens it belongs to.
We follow the ray that is parallel to the axis through the first lens and then through the focal point on the other side. This is shown in blue. A second ray that passes through the focal point in front of the lens, goes through the lens and is bent parallel to the axis. This is shown in red.
Where the two rays intersect we expect to find a real image being formed. That is indeed the situation and a real image is formed where these two rays and all the other rays striking the first lens converge. We will call this Image-1 or I1. As discovered before, this image is inverted and real. Because the object is close to the focal point, but far less than 2f, the image is also enlarged.
Now we go on to treat Image-1 as if it were a real object and deal with light rays coming from it entering lens 2. Take the parallel ray, an extension of the one we saw before. It goes through and is bent through the second focal point of the second lens.
We look at the ray which might have come from the first focal point of lens 2. This is shown in green for clarity. The lens will turn this ray so that it emerges parallel to the axis.
The two rays do not converge. Therefore there is no real image formed.
The rays which are diverging, can be traced back to their apparent origin. This is done below to find the location of the ultimate image, I2.
Notice that the first image produces an enlarged real image. Since that image is inside the focal point of the second lens, the second lens produces an enlarged virtual image. Thus both lenses take part in producing the very enlarged image.
Because the first, real image was inverted and because virtual images are not inverted compared to their original object, the final image remains inverted relative to the object.
Finally, I2 is further from us than I1. If an image is too close to our eyes, we cannot focus on it clearly. In practice, I2 may be formed as far away as the original object on the stage of the microscope. In that case, if we were to focus on the stage with one eye and at the same distance with the eye looking into the microscope, they would be balanced. This makes it easier on our optical system and thus is more relaxing to use.
So how do stereo microscopes work, the ones that we use both eyes and which don't invert the image? That will be a subject for the next edition.