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not able to focus at the same time two sets of parallel lines if the two sets are at right angles to each other.

616. Distortion of images. The image of a rectangular mesh, such as a piece of "hardware cloth," may show either of the two types of distortion shown in Figs. 419 and 420. The first of these is sometimes called barrelshaped distortion; the second, pincushion-shaped distortion. In the first case the center of the image is magnified more than the outer portions; in the second case the magnification is greater in the outer portions.

Distortion such as is shown in these figures can be controlled by the use of a properly placed diaphragm, or stop. In the photographic camera, if

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the diaphragm is placed in front (outside) of the lens, barrel-shaped distortion is produced; but if it is placed inside the lens (between the lens and the photographic film), pincushion-shaped distortion is produced. When the diaphragm is very close to the lens, no appreciable distortion is produced. A photographic lens which has its diaphragm so placed that there will be no distortion is called a rectilinear lens.

The type of distortion shown in Figs. 419 and 420 is usually prevented by placing a diaphragm close to the lens; if a combination of lenses is used, distortion is prevented by placing the diaphragm inside the combination.

PROBLEMS

1. A converging lens has a focal length of 30 cm. (a) Where will the image be when the object is 60 cm. from the lens? (b) 40 cm. from the lens? (c) 20 cm. from the lens? (d) Which of these are real images?

2. A converging lens of focal length 20 cm. has a virtual image 20 cm. from the lens. Compute the position of the object. 3. Solve Problem 2 by a graphical method.

4. An object placed 40 cm. from a converging lens has a real image 60 cm. from the lens. Compute the focal length.

5. An object placed 20 cm. from a converging lens has a virtual image 40 cm. from the lens. Compute the focal length.

6. A diverging lens has a focal length of - 20 cm. (a) Where will the image be when the object is 40 cm. from the lens? (b) 20 cm. from the lens?

7. Solve Problem 6 by a graphical method.

8. An object is 120 cm. from a screen and 20 cm. from a lens. What is the focal length of the lens if a real image is formed on the screen?

9. A lens having a focal length of 10 in. projects an image of a lantern slide on a screen 30 ft. from the lens. If the slide is 3 in. wide, how wide is the image?

10. A lamp and a screen are 120 cm. apart. What must be the focal length of a lens that will produce a real image of the lamp twice as large as the source?

11. A diverging lens placed 10 cm. from an object produces an image which is half the size of the object. Calculate the focal length of the lens.

12. An object is 60 cm. from a converging lens which has a focal length of 30 cm. A second converging lens, with a focal length of 10 cm., is placed 68 cm. beyond the first lens. Find the position of the final image.

13. A converging lens with a focal length of 40 cm. is placed 35 cm. from a diverging lens with a focal length of 10 cm. Compute the position of the image if the light from a far-distant object enters the converging lens first.

14. An optician places two thin lenses in contact. If one is + 1.25 dioptrics, and the other + 1.5 dioptrics, (a) what is the power of the combination? (b) what is the focal length of the combination?

15. (a) What is the power in dioptrics when a thin lens of - 1.25 dioptrics is placed in contact with a lens of +2.00 dioptrics? (6) What is the focal length of the combination?

16. If one has a lens of + 4.0 dioptrics and wishes to form a combination which will have a focal length of 1 m., what power should the second lens have?

17. An achromatic lens is made by combining a thin lens which has a focal length of + 12 cm. with another thin lens which has a focal length of-24 cm. What is the focal length of the combination?

CHAPTER XLIV

OPTICAL INSTRUMENTS

Introduction, 617. The photographic camera, 618. The eye, 619. The projection lantern, 620. The magnifying glass, 621. The compound microscope, 622. The astronomical telescope, 623. The terrestrial telescope, 624. The opera glass, 625. The prism binocular, 626. The reflecting telescope, 627. The range-finder, 628.

617. Introduction. It was shown in section 614 that mounting two lenses of certain kinds of glass together produces a combination which is, at least partially, corrected for chromatic aberration. It is shown in ad

D

FIG. 421

P

vanced treatises on lenses that all the different kinds of aberration can be approximately corrected by proper combinations of lenses. Hence, in most optical instruments, what is usually spoken of as a lens is in reality a group of lenses mounted together. Such a combination is equivalent to a single lens as far as the position and size of the image are concerned. It is best in elementary discussions of optical instruments to replace complicated combinations by simple lenses. Hence, in this text, instruments are usually simplified for purposes of explanation.

618. The photographic camera. In the photographic camera a converging lens forms a real, inverted image of the object on a sensitive plate, or film (P of Fig. 421), which is inclosed in a lighttight case. The figure shows a common combination of lenses for a camera. There are two pairs of lenses, and each pair is corrected for chromatic aberration. Between these, at D, is the diaphragm, or the stop, as it is often called. Such a combination of lenses forms a system which for convenience may be regarded as a single lens. The student should recall that images of objects which are at a great distance from a lens are focused at or near the principal focus, and that the images of near objects are focused some distance beyond the principal focus. Hence, in photographing distant objects the distance between the lens and the sensitized film is so adjusted that the film is at the principal focus of the lens system, but in photographing objects near at hand the lens must be moved farther from the film.

In the use of a camera having a short-focus lens, nearly all objects are relatively far away as compared with the focal length of the camera, and are imaged at or near the principal focus. In this case the camera may be focused once for all, giving a "fixedfocus camera," a common type in the cheaper grades. But in general the distance between

the plate and the lens must be adjusted to suit the distance of the object which is to be photographed.

FIG. 422

BA

B'A'

The stop in a camera lens serves several useful purposes. When it is placed at the center of the lens system, as shown in Fig. 421, the distortion referred to in section 616 is eliminated, and all straight lines in the object are imaged as straight lines. The lens is then a rectilinear one. When a relatively small-sized stop is used, the image becomes sharper. Not only is the spherical aberration decreased (sect. 613) but other types of aberration are at least partly remedied. A small stop is also of great assistance in bringing both near and distant objects into focus at the same time. When the stop of a lens is opened wide, only certain objects are in focus on the film for any one position of the lens. For example, when an object thirty feet away is in focus, objects nearer and farther away are out of focus, being often rather blurred, and the lens is said to have only a small depth of focus. When a small stop is used, objects both far and near become much more distinctly imaged, and the depth of focus is improved. This effect can be understood by the aid of Fig. 422. When the lens is wide open, the light from some object converging to some one point of the image in the plane A forms a large angle. In the plane B this light is spread over a considerable area; and if the plate were at B, the image would be blurred. When a small stop is used, the beams of light form small angles, and the light forming a point of an image in the plane A' will be spread over only a very small area if the plate is at B'. Hence the blurring of the image will not be so great in the position B' as in B. However, a small stop decreases the amount of light that reaches the photographic plate, or film, and hence a longer time of exposure is required.

619. The eye. The eye is in principle somewhat similar to the camera. A lens with its diaphragm, the iris, forms a real image on the retina, which is the screen at the rear. In the camera the focusing is done by moving the lens nearer or farther away from the plate or film; but in the eye the distance between the lens and the retina either is fixed or changes very little. The adjustment, or focus, in the eye is produced chiefly by changing the focal length of the lens by altering its curvature. This power of changing the shape of the lens of the eye is called accommodation. Older persons lose to some extent this power of accommodation, and need to wear glasses for reading, although they may see objects at a distance clearly and distinctly. What type of lens do they need for their glasses?

A shortsighted person can focus only on near objects, because the eye lens has too short a focal length, or because the distance between the lens and the retina is too great. By wearing diverging lenses the effective focal length of the combination of eye lens and glass lens is increased, and one can then see distinctly objects at a greater distance. When a person is farsighted, the focal length of the eye lens is too great, or the distance between the lens and the retina is too small, and he must wear converging lenses (the student should be certain that he understands why this type is necessary).

620. The projection lantern. Projection lanterns are now in common use. Not only are they used in classrooms and lecture rooms for projecting lantern slides but their use in connection with motion pictures has made them very popular. They contain two groups of lenses: L1, the condenser lenses, and L2, the projectionlens combination (Fig. 423). The projection lens L2 consists usually of two pairs of lenses or some other combination of lenses giving a system corrected for several types of aberration. The

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