If both lenses shown in Fig. 22 are considered thin, the centre c of the equi-convex lens is equidistant from both focal points ff'. In the positive meniscus, however, of the same focal length as the equi-convex lens, the centre c is seen to lie outside the lens itself, but its distance from the two focal points f and f' is still the same.

Suppose we place the equi-convex lens in a beam of parallel rays coming from a very distant object, such as the sun, and place a screen in the plane of the image, measuring the distance from the screen to the nearest surface of the lens and noting the size of the image, we shall find that on reversing the lens, the distance between lens and screen is exactly the same and the size of the sun's image is unaltered. In either case the distance between lens and screen is approximately equal to the focal length of the lens. In reality it is slightly less. If the thickness of the lens be considered, one-third of the thickness of the glass lens must be added. Placing now the meniscus lens in the sun's rays, we shall find that if these rays fall upon the convex side of the lens, the distance between the plane of the screen and the nearest surface of the lens is less than in the former case, but the size of the image remains the same. On reversing this lens and presenting the concave surface to the sun's rays, the distance between lens and screen is considerably greater than before, and greater than in the case of the equi-convex lens, but still the size of the image remains the same. The mean of the last two measurements is approximately equal to the focal length of the lens.

Fig.22.

The Formation Of Images By Positive Lenses 31

We can arrive very approximately at the focal length of either a single lens or a combination of lenses, by two measurements of the distance of the plane of the image (for parallel rays) for some fixed and convenient point in the lens or lens-mount, by presenting first one surface of the lens to the incident rays, and then the other, and taking the mean of the measurements.

The Formation Of Images By Positive Lenses 32

Fig.23.

We conclude this chapter by giving a method of determining very accurately the true focal length of any positive lens-system without involving calculation, but based upon a principle with which the reader is now familiar.

Mount the lens in a fixed position. Present the surface a of the lens to a beam of parallel rays and thus determine the position of the focal point f. Similarly present the surface b of the lens to a beam of parallel rays, and determine the position of the focal point f'.

Now place a screen at f with a mark or scale of definite length upon it, and a second screen for focusing at f'. Plumbed with the planes through f and f', on the base of the stand, fix two rules, as shown in the figure.

The distance between f and f' is only approximately double the focal length of the lens. Remove the screen s, with the definite marking upon it, rather less than half the distance between f' and f to the right of f, and move the focusing screen s' exactly the same distance to the left of f'. An indistinct image of the marking on s will now be seen on s'; proceed to move s and s' small, but exactly equal, distances in opposite directions, until the marking upon s is sharply defined and of equal size on s'. s and s' now occupy the positions for "unit magnifications," and we know that in this position each is removed the true 32

The Formation Of Images By Positive Lenses 33

Plate IV

Taken with a R. R. lens of 16-in. focal length at a distance of 4 ft., the short distance between lens and sitter has caused the mouth to be exaggerated in size, and the forehead to appear to recede. Compare Plate V. (By Mr. T. Habgood, Boscombe.)

The Formation Of Images By Positive Lenses 34

Plate V

Taken with the same 8 1/4" c. de v. lens combined with a 4-in. negative lens as employed for Plates II. and III., at a distance of 10 ft. The camera extension is chosen to produce the same size of head as in Plate IV. The image could have been made equally sharp, but the back of the positive element was unscrewed to illustrate the soft effect produced by introducing spherical aberration (see Fig 58). A picture showing this effect should be viewed at a considerable distance. (By the Author.) measure of the focal length from the focal points f and f' respectively. By plumbing at s and s' we thus read off on the rule the true focal length of the lens.

Notes

In Fig. 11 we have illustrated the manner in which a ray of light in passing from air through a plate of glass with parallel sides, emerges finally into air. Let us apply the laws of refraction to the case, in order to show that the incident and emergent rays are parallel to each other.

If we draw a normal pb p' to the surface of the glass at b at the point where the incident ray a b meets it, forming an angle with the normal, we shall find that after entering the second medium the ray will take an altered course b c, and that b c will form a different angle ф' with the normal at b. The law of refraction tells us that these two angles, termed the angles of incidence and refraction, are in the same plane, and that the sines of these angles bear to one another a constant ratio, depending solely upon the relation of the refractive indices of the two media. Calling the refractive index of air unity, and that of glass the Greek letter ц, sin ф = ц sin ф' is a constant for these two media; and in general, in passing from one medium of refractive index ц to another of refractive index ц', ц sin ф =ц'sinф'