Lenses are not only used to correct vision defects.  Sometimes our vision, as normal as it may be, is not as good as we might like for the job at hand. For example, if we wish to examine the details of a very small (microscopic) organism, we may try to look at it as closely as we can with our naked eye, but chances are we will not be able to see the detail desired. In such a case, lenses can be used to enhance our eye’s vision.

A compound microscope is an instrument that allows us to view a small object as if it were very close to us.  This is effectively accomplished by forming an image that is magnified and placed far away (so  your eye can be relaxed when viewing the final image). Such a microscope uses two converging lenses to accomplish the desired effect. The basic set-up is shown in the figure below.

Figure 3.2

The object being viewed is placed just outside the focal length of the objective lens (the lens closest to the object). From the thin lens equation, we then get that the image thus formed is real, inverted, and enlarged.  (Can you show this?)  We will call this image the intermediate image since it is not the final image viewed in the eyepiece.

We now treat the real intermediate image from the objective lens as the object for the eyepiece.  From Fig. 3.2 we can see that the object distance for the eyepiece, D_o,eye, is equal to the separation between the objective and eyepiece lenses, S, minus the image distance from the objective lens, D_i,obj.  The eyepiece lens is then positioned so that the intermediate image is just inside the eyepiece’s focal point.  This will make the final image virtual and enlarged, with the rays emerging from the eyepiece being nearly parallel (since, by definition, the  emerging rays would be parallel if the object for the lens were at its focal point!). That the emerging rays from the eyepiece are nearly parallel is important, since then the eye can be relaxed when viewing the image.  (Remember that the ciliary muscle has to tense to focus the eye on objects as they move in from infinity.) The final image will then be greatly enlarged compared to the original object.

As a specific example, consider a compound microscope with the following characteristics.

An object is placed on a microscope slide that is then positioned 13.0 mm from the 12.0-mm focal length objective lens. The separation between the objective lens and the eyepiece is 20.0 cm.  The eyepiece has a focal length of 50.0 mm.

The object on the microscope slide is the object for the objective lens.  We will therefore denote the object distance as D_o,obj, which is equal to 13.0 mm.  Since the object is a real object (it is actually placed there, so light must be diverging from it!), the object position for the objective lens is d_{o, obj} = +13.0 mm.  The objective lens is a converging lens, so its focal length is f_obj = +12.0 mm.  From the thin lens equation, we then get that the image position for the objective lens is d_i,obj = 156 mm, so that the magnification of the objective lens is m_obj = – d_i,obj / d_o,obj = –12.  The image is thus real (d_i,obj > 0), enlarged (|m| > 1), and inverted (m < 0), as advertised above.

We now treat the image from the objective lens as the object for the eyepiece. The image distance for the objective lens is D_i,obj = 156 mm.  The separation between the two lenses is S = 200 mm.  The distance between the image for the objective lens (the new object for the eyepiece) and the eyepiece is therefore (see Fig. 3.2) D_o,eye = S – D_i,obj = 44.0 mm.  Light rays are diverging as they approach the eyepiece (draw a diagram with some rays if you don’t believe this!), so the object position for the eyepiece is positive: d_o,eye = +44.0 mm.  Using this information along with the focal length for the eyepiece, f_eye = +50.0 mm, we get that the image position for the eyepiece is d_i,eye = –367 mm, with a corresponding magnification of m_eye = –d_i,eye / d_o,eye = +8.3.

The total magnification of the compound microscope is therefore m_total = m_obj m_eye = –100.  This tells us that the final image viewed in the eyepiece is one hundred times larger than the original object, and it is inverted relative to the original object (which we tend not to notice in a microscope).  The image distance for the eyepiece, d_i,eye = –367 mm, tells us that the  final image is 367 mm behind the eyepiece (it looks like it’s big and inside the microscope tube), and is virtual.

This is not an easy discussion.  Please work carefully through the argument above, making sure that you understand the reasoning behind each step that is performed.  If you can really understand this reasoning and how this microscope works, then you have really come a long way in understanding thin lenses!