[Ill.u.s.tration: FIG. 376.--Formation of a spherical lens.]

There are two cla.s.ses of lenses: those thick in the middle are called _convex_, while those thick at the edges are _concave_. The mode of constructing the six forms of spherical lenses is shown in Fig. 377.

These are named as follows: (1) double convex, (2) plano convex, (3) concavo-convex, (4) double concave, (5) plano concave, (6) convexo-concave.

[Ill.u.s.tration: FIG. 377.--Forms of Lenses. 1. double convex; 2. plano convex; 3. concavo convex; 4. double concave; 5. plano concave; 6.

convexo concave.]

[Ill.u.s.tration: FIG. 378.--The action of a burning gla.s.s.]

=384. Effect of Lenses upon Light.=--The most important characteristic of a lens is its effect upon a beam of light. Most persons have seen a "burning gla.s.s," a double convex lens, used to bring to a point, or focus, a beam of sunlight. To show the action of a burning gla.s.s send a beam of light into a darkened room, and place in its path a double convex lens. (See Fig. 378.) If two blackboard erasers are struck together near the lens, the chalk particles in the path of the light are strongly illuminated, showing that the light after pa.s.sing through the lens it brought to a focus and that it spreads out beyond this point.

This point to which the cone of light rays converges after pa.s.sing through the convex lens is called the _princ.i.p.al_ focus of the lens. The distance from the princ.i.p.al focus to the center of the lens is the _focal length_ or _princ.i.p.al focal distance_ of the lens. _The focal length of double convex lenses of crown gla.s.s is about the same as the radius of curvature of either surface._ The action of a convex or converging lens upon light may be better understood by studying Fig. 379 in which light is pa.s.sing from _S_ to _F_. The successive positions and shape of the advancing light waves are indicated by lines drawn across the beam. The light being r.e.t.a.r.ded more in the thicker part of the lens, the light waves on leaving the lens have a concave front. Since light waves tend to move at right angles to the front of the wave, the light is brought to a focus. After pa.s.sing the focus the waves have a convex front, forming a diverging cone.

[Ill.u.s.tration: FIG. 379.--Wave diagram of light pa.s.sing through a convex lens.]

=385. Concave Lenses.=--When sunlight pa.s.ses through a _concave_ lens a diverging cone of light is formed. (See Fig. 380.) This is caused by the edges of the wave being r.e.t.a.r.ded more than the center, producing a convex wave front. This diverging cone of light acts as if it had proceeded from a luminous point at _F_.

This point is called a _virtual_ focus and is nearly at the center of the curvature of the nearer surface.

[Ill.u.s.tration: FIG. 380.--Wave diagram of light pa.s.sing through a concave lens.]

=386. The Formation of Images by Lenses.=--If a beam composed of _parallel_ rays of light, as sunlight, is sent in turn through three convex lenses of the same diameter but of different thickness, it is found that the _thicker the lens the greater is its converging power, or the shorter is its focal_ length. (See Fig. 381.) Now if a luminous body, such as a lighted candle, be placed near the convex lens but _beyond its focal length_, the light will be brought to a focus upon the other side of the lens and an image of the candle may be clearly seen upon the screen placed at this point. (See Fig. 382.) _The two points so situated on opposite sides of a lens that an object at one will form an image at the other are called conjugate foci._

[Ill.u.s.tration: FIG. 381.--The thicker the lens, the shorter is its focal length.]

[Ill.u.s.tration: FIG. 382.--_C_ and _S_ are at conjugate foci.]

It will be helpful to compare the images formed of a candle by an _aperture_ and by a _convex_ lens. Rays of light from each point of the luminous body pa.s.s through the aperture in straight lines and produce upon the screen a lighted s.p.a.ce of the same shape as the candle. This image is rather _hazy_ in outline. Each cone of rays from luminous points of the flame is brought by the lens to a focus on the screen, producing a _sharp image_. It is the converging power of convex lenses that enables them to produce clear images.

[Ill.u.s.tration: FIG. 383.--Construction of a real image by a convex lens.]

=387. The Construction of Diagrams to Represent the Formation of Images by Lenses.=--Just as the earth has an axis at right angles to its equator to which are referred positions and distances, so a lens has a _princ.i.p.al axis_ at right angles to its greatest diameter and along this axis are certain definite positions as shown in Fig. 383. Let _MN_ be the _princ.i.p.al axis_ of a convex lens, _P_ and _P'_ are _princ.i.p.al foci_ on either side of the lens, _S_ and _S'_ are _secondary foci_. These are at points on the princ.i.p.al axis that are twice as far from _O_, the center of the lens, as are the princ.i.p.al foci. In the formation of images by a convex lens, several distinct cases may be noticed:

(A) If a luminous body is at a _great distance_ at the left, its light is brought to a _focus_ at _P_, or its _image is formed at P_. (B) As the _object approaches_ the lens the _image gradually recedes_ until the object and image are at _S_ and _S'_, _equally distant from O and of equal size_ (as in Fig. 383). The object and image are now said to be at the _secondary foci_ of the lens. (C) As the _object moves from S to P_ the image recedes, rapidly increasing in size until (D) when the object is at _P_ the rays become parallel and no image is formed. (E) When the object is between _P_ and the lens, the rays _appear to proceed from points back of the object_, thus forming an _erect, larger, virtual image_ of the object. (See Fig. 384.) This last arrangement ill.u.s.trates the _simple microscope_.

With a concave lens but one case is possible, that corresponding to the one last mentioned with convex lenses; since the rays from a body are divergent after pa.s.sing through a concave lens they appear to proceed from points _nearer_ the lens than the object and hence a _virtual, erect, smaller image_ of the object is formed. This virtual image may be seen by looking _through_ the lens toward the object. (See Fig. 385.)

[Ill.u.s.tration: FIG. 384.--Construction of a virtual image by a convex lens.]

[Ill.u.s.tration: FIG. 385.--Construction of a virtual image by a concave lens.]

=388. The Lens Equation.=--The location of either the object or of the image upon the princ.i.p.al axis of the lens may be calculated if the position of one of these and the focal length are known. This is accomplished by the use of a formula 1/_F_ = 1/_D_{0}_ + 1/_D_{1}_ in which _F_ represents the focal length and _D_{0}_ and _D_{1}_ the distance from the lens of the object and the image respectively. Thus if an object is placed 30 cm. from a lens of 10 cm. focal length, where will the image be formed? Thus: 1/10 = 1/30 + 1/_D_ and 3_D_{1}_ = _D_{1}_ + 30, or 2_D_{1}_ = 30 _D_{1}_ = 15. This result indicates that a real image will be 15 cm. from the lens. A minus value would indicate a virtual image.

Important Topics

(A) Lenses: convex, concave, six forms, center and radius of curvature.

(B) Princ.i.p.al focus, focal length, virtual focus, conjugate foci.

(C) Princ.i.p.al axis, images formed when object is in various locations.

(D) Computation of location of images.

Exercises

1. Why is an image of a candle formed by an aperture, not sharply defined?

2. When a photographer takes your picture and moves the camera nearer you, must he move the ground gla.s.s screen toward the lens or away from it? Explain.

3. How can you find the princ.i.p.al focal length of a lens.

4. How can you test a spectacle lens to see whether it is convex concave?

5. When will a convex lens produce a virtual image? Have you ever seen one? Where?

6. When a photographer wishes to obtain a full length view of a person, where does he place the camera?

7. The focal length of the lens is 24 cm. How far from the lens must an object be placed in order that a real image may be three times as long as the object?

8. There is a perfect image of an object on the ground gla.s.s of a camera. The center of the lens is 20 cm. in front of the image and the object 75 cm. from the lens. What is the focal length of the lens?

9. An object is 60 cm. from the lens, the image 120 cm. from it. Find the focal length.

10. How can you find experimentally the princ.i.p.al focal length of a lens?

11. A lens is used to project an enlarged image of a candle upon a screen. Which is farther from the lens, the candle or the image?

Explain.

(6) OPTICAL INSTRUMENTS

=389. The Eye.=--The most common optical instrument is the _eye_. While the structure of the eye is complicated, the principle of it is simple, involving the formation of an image by a double convex lens. (See Fig.

386, in which is shown a front to back, vertical cross-section of the eye.) The eye appears to be made of portions of two spheres, one of which, smaller than the other, is placed in front. This projecting part is transparent, but refracts the light which strikes it obliquely, so as to turn it into the eye. This enables us to see objects at the side when looking straight ahead. Test this by looking directly in front of you and see how far back on each side of the head you can notice a movement of the forefinger of each hand.

[Ill.u.s.tration: FIG. 386.--Cross-section of the eye.]

=390. Action of the Eye in Vision.=--When we look at an object, a small, real, inverted image is formed upon the _retina_ at the back of the interior of the eye. The retina is an expansion of the optic nerve and covers the inner surface at the back of the eyeball. Seeing is due to the action of light in forming images upon the retina. Our eyes are so constructed that when they are relaxed the lens is adjusted to form clear images of _distant_ objects upon the retina. If we look from distant to near objects without changing the shape of the eye lens, a sharp image of the latter cannot be formed and we get a blurred impression. It is difficult, however, to look at objects without automatically adjusting the eye lens so that it will make a sharp image.

Test this by looking out of a window at a distant object, then without moving the head or eyes look at the gla.s.s of the window; you will notice a slight change of some sort _in_ the eye itself as the vision is adjusted. This adjustment is made by muscles that pull or compress the eye lens so as to make it thicker for near objects and thinner for distant ones. The eye ordinarily does not see objects nearer than 10 in.

clearly. This means that the greatest possible thickening of lens will not form clear images upon the retina if the object is nearer than 10 in. (25 cm.).

[Ill.u.s.tration: FIG. 387.--The visual angle, _AOB_ is greater at _AB_ than at _A'B'_.]

=391. The Visual Angle.=--To examine objects carefully we usually bring them as close to the eye as possible, for the nearer to the eye the object is brought, the larger is the visual angle formed by it (see Fig.

387), and the larger is its image upon the retina. _The visual angle of an object is the angle at the eye lens between the rays that have come from the ends of the object._ Consequently the more distant the object, the smaller is its visual angle. Now if we wish to examine small objects with great care, we frequently find that it is necessary to bring them close to the eye so that they have a visual angle of adequate size. If they must be brought closer than 10 in. a double convex lens is placed in front of the eye. This a.s.sists the eye lens in converging the light so that a clear image may be formed when the object is close, say an inch or so from the eye. This is the principle of the magnifying gla.s.s used by watch-makers and of the _simple microscope_. The action of the latter is ill.u.s.trated by Fig. 388. The convex lens forms a virtual, enlarged image "_A'-B'_" of the object "_A-B_" which it observed instead of the object itself.

[Ill.u.s.tration: FIG. 388.--Action of the simple microscope.]