Introduction: If there were two scientific instruments which propelled experimental science forward in the late Renaissance they are the microscope and the telescope. They were some of the first sensor devices capable of amplifying human senses. I have excerpted a short history of each from The Software Toolworks Illustrated Encyclopedia:
"Magnification by simple lenses has been known from ancient times,
but the development of the modern microscope dates from the construction
of compound-lens systems, which occurred some time in the period between
1590 and 1610. The credit should probably go to the Dutch lensmakers
Hans and Zacharias Jannsen (father and son), who in about 1600 constructed
a simple instrument made of a pair of lenses mounted in a sliding
tube. A compound-lens system using a convex lens in the eyepiece was
described by Johannes Kepler in 1611, probably deriving from the Jannsens'
"Tradition attributes the invention of the telescope to the accidental
alignment of two lenses of opposite curvature and diverse focal length
by Hans Lippershey in Holland in 1608. The principle, however, may
have been known to Roger Bacon in the 13th century and to the early
spectacle makers of Italy.
"Galileo Galilei constructed (1609) the first lens, or refracting,
telescope for astronomical purposes. Using several versions, he discovered
the four brightest Jovian satellites, lunar mountains, sunspots, the
starry nature of the Milky Way, and the apparent elongation of Saturn,
now known to be its rings. Galileo's simple lenses suffered from a
variety of aberrations, or defects of image formation: chromatic aberration,
or the variation of focal length with color; spherical aberration,
the variation of focal length with distance of parallel rays from
the lens axis; coma, the increasing blur of a point image with angle
of the rays to the axis; and distortion, the imaging of straight lines
in the object as curves. These aberrations were minimized in a variety
of ways. Christiaan Huygens constructed extremely long aerial telescopes
in which the objective lens was mounted on a pole and connected to
the eyepiece by only a taut wire. Despite extraordinary difficulties,
such instruments achieved useful results, especially in lunar mapping.''
These instruments have progressed far beyond the simple devices described above, but our study will deal only with the basic versions, using only convex (converging) lenses.
Theory: There are two principles essential to these instruments. First; light bends when moving from one medium to another. Second; the image formed by one lens can be the object for another.
1) The whys of the bending of light were described in a previous lab. However, that experiment dealt with planar surfaces. A lens has at least one spherical section as a surface. With planar or rectangular lenses the exit light ray is parallel to the incident ray; it is merely offset. See figure 1:
On the other hand, when a ray of light is incident on a spherical lens it is redirected. According to Snell's law the ray must be bent toward the normal when traveling from a less to a more optically dense medium. The normal is drawn tangent to the surface of the lens where the ray enters. See figure 2a. When the ray exits to a less optically dense medium it is bent away from the normal drawn to the tangent. See figure 2b.
The effect is to focus parallel rays of light to a point. See figure 3:
Moreover, due to symmetry, if the rays originate from a point the lens will cause them to be parallel; merely reverse the rays direction in figure 3. (There is a great deal of symmetry between telescopes and microscopes: one is the conjugate of the other.)
How much of a change of direction the light rays experience is dependent upon the curvature of the lens surface. Greater curvature causes greater bending. Lenses are normally characterized by the amount of bending, not by their curvature. Where two incident parallel rays which are subsequently bent cross is called the focal point, and the distance from the lens to this point is called the focal length. We rate lenses by their focal length, as in a long or a short focal length lens. Microscopes and telescopes employ both.
One can determine a focal length (f) by examining the distance (s) to an object seen through the lens and the distance (s') to the image formed. A simple equation, called the lensmakers' equation, generates the focal length:
eq. 1It will be necessary to ascertain the focal lengths of the various lenses you will use. N.B.: Some texts replace s and s' with p and q; be flexible!
2) Unlike most human beings, a lens doesn't know if what it `sees' is a physical reality or a mere projection. Therefore if one lens produces an image a second lens can treat this as an object. The difference between a microscope and a telescope is where the object for that first lens, called the objective, is in relation to the lens. This relation determines where the image formed by the first lens will be formed. For instance, if the object for the first lens is a long way away, the image will be formed on the opposite side of the lens. When, for a converging lens, the image is formed on the opposite side of the lens from the object s' is positive. You can verify this with equation 1: make s > f. On the other hand, if the object is close to the lens, the image will be formed on the same side of the lens as the object. Here s' < 0.
A small image (or object) one meter away emits (or reflects) light in parallel rays to your eyes. Your eye is most comfortable viewing objects perhaps a meter away; there is little strain to see detail and the image is clear. Optical instruments should therefore produce an image to your eye that is about one meter distant (a ballpark figure).
Now the obvious difference between the function of a microscope and the function of a telescope is that the former views small things close up and the latter views large things far away. In both cases we want a comfortable image for the viewer's eye. For these reasons a microscope uses a short focal length objective and a telescope uses a long focal length objective.
With a microscope we place a sample close to a short focal length lens, just beyond its focal point. This produces an image on the other side of the objective. We then use a second, longer focal length lens, called the eyepiece, to view this image. The image formed by the objective is just inside the focal length of the eyepiece. The image the eyepiece forms is therefore in front of the lens. This serves the purpose of moving the "virtual'' object the eye sees to a comfortable distance while magnifying it. (Magnification for a single lens is determined by the negative ratio of s' to s, or alternatively, the height of the image to the height of the object). The spacing (L) between the lenses is critical; L must be slightly less than s' (for the objective) plus f for the eyepiece. Since s is approximately equal to f for the objective, with the lensmakers' equation and f for the eyepiece L can be determined. Small adjustments to focusing are made by small variations in L.
A telescope works in the opposite manner. The long focal length objective forms its image such that s' = f for the objective. This is due to the fact that s is infinite (or close enough) for a telescope. The eyepiece, a shorter focal length lens, focuses on this image. The distance between the lenses is exactly the sum of the two lenses' focal lengths, so s = f for the eyepiece. The eye sees an image at infinity (greater than a meter), which is a comfortable viewing position. The magnification in a telescope is the ratio of the focal lengths (objective over eyepiece obviously).
There are other kinds of microscopes and telescopes--electron microscope, reflecting telescope--but we will restrict ourselves to 'scopes explained above.
Build a microscope
Build a telescope
-If you let the object distance go to infinity, finding the focal length should be easy.