normal. The normal of any emergent ray is an imaginary line at right angles to the surface of the lens at the point where the ray emerges from the lens.

e. Divergent Lens. A lens of a different type can be approximated by placing two prisms apex to apex (fig. 33). If rays of light strike the front surfaces of the prisms, the rays will pass through and, in accordance with the law of refraction, those passing through the upper prism will travel upward, while those passing through the lower prism will travel downward. Now assume that the front and rear surfaces of this pair of prisms have been rendered spherical and

Figure 33-Deviation of Rays by Two Figure 34-Deviation of Rays by Divergent Prisms, Apex to Apex

Lens

that the two prisms have been converted into a lens (fig. 34). All rays of light except the axial ray passing through this lens would spread out or diverge, but instead of splitting in two at the axis would diverge evenly in a spherical manner. This type of lens is known as a divergent lens. (All divergent lenses are thicker at the edges than at the center.)

a.

18. TOTAL INTERNAL REFLECTION AND CRITICAL ANGLE. When light passing from air into a more dense medium, such as glass, strikes the boundary surface, it is refracted. This occurs regardless of the incident angle. However, when light attempting to leave a more dense medium for a less dense medium strikes the boundary surface, it may be reflected, rather than refracted, even though both mediums are perfectly transparent. This is known as total internal reflection and occurs when the incident angle exceeds

a certain critical angle. The critical angle depends upon the density of the medium. Critical angles for various substances are listed in paragraph 19.

b. The total internal reflection of light can be illustrated by following the rays from a light source under water. Water has a critical angle of 48 degrees 36 minutes. Rays of light from such a source would be incident at various angles on the surface separating the water and air (fig. 35). As the angle of incidence of the light rays increases, the deviation of the refracted rays becomes proportionately greater. A point is reached where an incident ray is deviated to such an extent that it travels along the surface of the water and does not emerge into the air. The angle formed by this incident ray and the normal is the critical angle of the medium.

C. All rays traveling in a dense medium and striking the surface with an angle of incidence that is less than the critical angle of the medium are refracted and pass into the lighter medium in accordance with the laws of refraction. All such rays striking at an angle of incidence greater than the critical angle of the medium are reflected in accordance with the laws of reflection.

d. The critical angle has a practical application in the design of prisms used in fire control instruments. In such instruments, it is quite often necessary to change the course of the path of light. This deviation could be accomplished by mirrors but the prisms used perform the task more satisfactorily. When prisms are employed that have angles greater than the critical angle of the substance of which they are made, their reflecting surfaces do not require silvering, yet these surfaces appear to be silvered when one looks into such a prism.

e.

Properties of Light

Consider a prism with two faces at right angles and a back or hypotenuse at a 45-degree angle (fig. 36). An incident ray, striking one of the right-angle faces at the normal, passes into the prism without refraction or deviation until it hits the boundary of the medium (back of the prism). Since the angle of the back is 45 degrees and the critical angle of the glass of the prism is 42 degrees, the ray cannot pass through the back surface of the prism. Instead, it is totally reflected. Inasmuch as the angle of incidence between the incident ray and the normal (at the back surface) is 45 degrees, the angle of reflection would be the same because these angles are always equal. The result is that the ray is reflected a total of 90 degrees, strikes the surface of the other right-angle face of the prism at the normal, and passes out of the prism without further deviation.

19. CRITICAL ANGLES OF VARIOUS SUBSTANCES.

a. The critical angles for various substances, when the external medium is air, are as follows:

b. The small critical angle of diamond accounts for the brilliance of a well-cut diamond. It is due to the total internal reflection of light which occurs for a greater variety of angles than in any other substance. The light entering the diamond is totally reflected back and forth a number of times before emerging, producing bright multiple reflections.

Section IV

IMAGE FORMATION

20. GENERAL.

a. In considering the principles of the formation of images by lenses, for simplicity of explanation it will be assumed that perfect single lenses are used.

21. CLASSIFICATION OF IMAGES.

a.

Virtual and Real Images. Two types of images are produced by optical elements, virtual images and real images.

(1) VIRTUAL IMAGES. A virtual image is so called because it has no objective or real existence. It exists only in the mind and cannot be thrown upon a screen because it is apparent only to the eyes of the observer. A familiar example is the virtual image formed by a mirror. The image of the person looking into the mirror appears

to be on the other side of the mirror (fig. 37). No trace of the image can be seen on the back of the mirror.

(2) REAL IMAGES. A real image actually exists. It can be thrown upon a screen. The lenses of the human eye and the camera form real images. The real image formed by a camera can be seen on the ground glass (fig. 38).

b. Erect, Inverted, Normal, and Reverted Images. When an image is reflected or refracted by optical elements, the parts of the object are seen as being transposed horizontally, vertically, or both. This is illustrated by what happens to the letter "F" (fig. 39).

(1) An image, regardless of size, that shows the face of an object unchanged is said to be normal and erect (fig. 39A). When the object is seen as horizontally transposed through 180 degrees, it is termed reverted and erect (B, fig. 39). Reversion is the effect seen in a mirror where the image is reversed so that the right side of the object becomes the left side of the image (fig. 37).

(2) The image of an object with its face unchanged but upside down is termed normal and inverted (C, fig. 39). If it appears turned from left to right as well as upside down, it is said to be reverted and inverted (D, fig. 39). Inversion is the effect seen on the ground glass of a camera (fig. 38). Such an image is normal and inverted.

C. The most satisfactory method of visualizing the positions in which an image may be transposed is by cutting a letter "F" out of paper and marking the face and reverse sides "NORMAL" and "REVERSED," respectively. If the normal erect letter (A, fig. 39) is inverted bottom side up without turning it over, it will appear as in C, figure 39. If it is then turned over or "inverted" sideways, it will appear reverted and inverted (D, fig. 39).