»io6 THEORY OF OPTICS
element to the picture. From the focal length of the objective, the length of the tube, and the focal length of the eyepiece which is just sufficient to bring out the detail in the image, it is possible to calculate from (5) the smallest permissible magnification for complete resolution. This magnification is greater the greater the resolving power of the objective. Assuming a perfect objective, the necessary magnification of the whole instrument depends only upon the numerical aperture. This has not yet been pushed beyond the limit (for immersion systems) a == 1.6. Hence, by equation (87) on page 92, the smallest interval d which can be optically resolved is
, A. 0.00053 mm. £
d — — =-------—-------= o.oooio mm.
2.a 3.2
if A. be the wave-length of green light. Now at a distance d = 25 cm. 'from the eye an interval d' = 0.145 mm. has a visual angle of 2', which is the smallest angle which ean be easily distinguished. Since d': d= 905, the limit of resolution of the microscope is attained when the total magnification is about poo. Imperfections in the objective reduce this required magnification somewhat. By equation (85) on page 89 the ratio of the brightness of the image to the normal brightness is for this case
„ „ <52-<z2 mo-i.6\2 i
2-900 / 20'
the radius p of the pupil of the eye being assumed as 2 mm.
h. Experimental Determination of the Magnification and the Numerical Aperture.—The magnification may be determined by using as an object a fine glass scale and drawing with the help of a camera lucida its image upon a piece of paper placed at a distance of 25 cm. from the eye. The simplest form of camera lucida consists .of a little mirror mounted obliquely to the axis of tibe instrument, from the middle of which the silvering has been removed so as to leave a small hole of about 2 mm, diameter. The image in the microscope is seen through the bring out completely the detail in the image formed by the objective. A stronger magnification may-indeed be conveniently used in bringing out this detail, but it adds no newhe edge of the field of view becomes sharply defined,ly the domain of geometrical optics.