Again considering the formula v + u we see that as u increases, v decreases, so that as the object recedes from the lens the image approaches it. When u is less than f a virtual image is formed, but with this we are not concerned.
It can also be shown that the relative sizes of image and object are in the ratio v : u, so that the magnification or reduction is The solution of some examples will make clear the use of these formula:.
Example 1.A 6 in. lens is sharply focussed on an object distant fo ft. What is the distance of the lens from the plate? Here/ =1 (,05 in. is ft.) u = IO and v is required.
Substituting these values in = we have 10 = v 2, 19 so that = v to and v = Example 2.It is desired to enlarge from quarter-plate to whole-plate with a 6 in. lens. What must be the distance of the paper and negative respectively from the lens ? In this case the magnification is 2, so that = 2.
Substituting in = - v u f we have 2U U so that = 2 211 and u = ft. v = ft.
Example 2 is another form of the frequently occurring question in which it is desired to know whether a lens of given focus can be used in a studio of certain length to obtain portraits of a particular size.
Field of angle of view included by a lens of focal length f when used with a plate whose longer side is n can easily be found by drawing a right-angled triangle, in which the sides subtending the right angle are f and 71 n The angle opposite the side of length is half 2 2the angle of view, and its value can easily be ascertained by measurement with a protractor. When the focal length
of a lens is the same or less than the shorter side of the plate it is used with, it is a wide-angle lens for that plate. Obviously it could be used on a smaller plate, and would not then include such a large field of view. A normal angle of view would be included by a lens of focal length about equal to the diagonal of the plate. Lenses of longer relative focal length are known as long-focus or narrow-angle lenses. It must be remembered that the resulting picture will be the same if it is taken with a wide-angle, medium-angle, or narrow-angle lens of the same focal length on the same plate. The wide-angle and medium-angle lenses can, how ever, be used with larger plates, and so have a more extended field of usefulness. As an example it may be mentioned that a 6 in. lens can be obtained which will sharply cover a whole plate at full aperture. Such a lens is, however, of suitable focal length for use on a 5 x 4 in. plate as a medium-angle lens. The medium-angle 6 in. lens recom mended for a 5 x 4 in. plate will, however, not be suitable for use on a whole plate, because it will not illuminate it all over. The angle of the cone of rays transmitted by different lenses of the same focal length is not the same, owing to the different constructions and mountings employed. That transmitted by the 6 in. wide-angle lens is much' greater than the angle of the cone of rays transmitted by the medium angle lens. (It may here be mentioned that the perspective of a picture becomes more pleasing as the focal length of the lens increases.