Part 62 (1/2)

[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.