Page:Handbook of Ophthalmology (3rd edition).djvu/20

14 as in the case of the principal focal distance, is expressed by a fraction whose numerator is one, and whose denominator is the distance of the points $$a$$ and $$\alpha$$ respectively from the centre of the lens. The optical significance of the object-point is expressed by $$\frac{1}{a}$$, that of the image-point by $$\frac{1}{\alpha}$$. We obtain in this way three optical values, whose relation to each other is expressed by the formula $$\frac{1}{a} + \frac{1}{\alpha} = \frac{1}{f}$$. By this formula, when two values are given, we obtain the third.



If we have, for instance, a camera obscura with a lens of 4 inches focal length, while the screen lies not at the principal focus of the lens, but at 5 inches from the centre of the lens, we have given the values of $$f$$—i.e., the principal focal length—and $$\alpha$$,—i.e., the distance at which the image is to be thrown. The formula $$\frac{1}{a} + \frac{1}{\alpha} = \frac{1}{f}$$ becomes $$\frac{1}{a} + \frac{1}{5} = \frac{1}{4}$$ that is, $$\frac{1}{a} = \frac{1}{20}$$. The object must therefore be at a distance of 20 inches in order to cast its image on the screen, or in other words, the camera obscura is adjusted for a distance of 20 inches.

So it is with the eye which is adjusted for a determinate finite distance, either by the action of its accommodation or by its optical structure. The latter is the case in the short-sighted eye.

The third possibility is, that the screen of the camera obscura may lie within the focal distance of the lens. For what distance is the instrument now adjusted? where must the object be placed to cast its image on the screen?

We have seen that objects at a finite distance cast their images beyond the principal focus. The further the object is removed the nearer its image approaches the principal focus, and finally, when the object is at an infinite distance, its image is formed exactly at the principal focus of the lens. An object cannot be at a greater than an infinite distance; therefore a camera obscura, whose screen lies within the focal distance, can exhibit no distinct pictures. Since this condition actually exists in the hypermetropic