Page 327 - Modern Optical Engineering The Design of Optical Systems

306 Chapter Thirteen

inverted image (usually enlarged) of the object. The eyelens reimages
the object at a comfortable viewing distance and magnifies the image
still further. The magnifying power of the system can be determined
by substituting the value of the combined focal length of the two com-
ponents (as given by Eq. 4.5) into Eq. 13.10a
f f
e o
f (13.11)
eo f f d
e o
10 in (f f d) 10 in
o
e
MP
f f f
eo e o
The more conventional way to determine the magnification is to
view it as the product of the objective magnification times the eyepiece
magnification. With reference to Fig. 13.12, this approach gives
s 10 in
MP M M 2 (13.12)
o e
s f
1 e
Equations 13.11 and 13.12 yield exactly the same value of magnifica-
tion, as can be shown by substituting (d f e ) for s 2 ; determining s 1 in
terms of d, f e , and f o (from Eq. 2.4); and substituting in Eq. 13.12 to get
Eq. 13.11.
An ordinary laboratory microscope has a tube length of 160 mm. The
tube length is the distance from the second (i.e., internal) focal point
of the objective to the first focal point of the eyepiece. Thus, by Eq. 2.6,
the objective magnification is 160/f o , and rewriting Eq. 13.12 for
millimeter measure, we get
160 254
MP (13.13)
f f
o e
Standard microscope optics are usually referred to by their power.
Thus, a 16-mm focal length objective has a power of 10 and an 0.5-in
focal length eyepiece has a power of 20 . The combination of the two
would have a magnifying power of 200 , or 200 diameters.
The resolution of a microscope is limited by both diffraction and the
resolution of the eye in the same manner as in a telescope. In the case
of the microscope, however, we are interested in the linear resolution
rather than angular resolution. By Rayleigh’s criterion, the smallest
separation between two object points that will allow them to be
resolved is given by Eq. 9.16
0.61
Z
NA

where is wavelength and NA n sin U, the numerical aperture of the
system. Note that the index n and the slope of the marginal ray U
are those at the object. Because of the importance of the numerical