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is convex, the image is nearer to it than is the point, while if it is concave, the image, if formed behind the mirror at all (that is, if it is virtual), is farther from the mirror than is the point.

445. Construction of image of object in a plane mirror. The image of an object in a plane mirror (Fig. 416) may be located by applying the law

proved above for each of its points, that is, by drawing from each point a perpendicular to the reflecting surface and extending it an equal distance on the other side.




FIG. 416. Construction of image of object in a plane mirror

To find the path of the rays which come to an eye placed at E from any point of the object, such as A, we have only to draw a line from the image A' of this point to the eye and connect the point of intersection of this line with the mirror, namely C, with the original point A. ACE is then the path of the ray.

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Let a candle (Fig. 417) be placed exactly as far in front of a pane of window glass as a bottle full of water is behind it, both objects being on the same perpendicular drawn through the glass. The candle will appear to be burning inside the water. This explains a large class of familiar optical illusions, such as the "figure suspended in mid-air," the "bust of a person without a trunk," the stage ghost," etc. In the last case the illusion is produced by causing the audience to look at the actors obliquely through a sheet of very clear plate glass, the edges of which are concealed by draperies. Images of strongly illuminated figures at one side then appear to the audience to be in the midst of the actors.


FIG. 417. Position of image

in a plane mirror

446. Focal length of a curved mirror half its radius of curvature. The effect of a convex mirror on plane waves incident upon it is shown in Fig. 418. The wave which would at a

given instant have been at co,d is at co,d, where 00,

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The center F from which the waves appear to come to the

eye E is the focus

of the mirror.

Now so long as the arc cod is

small its curvature may, without appreciable error, be measured by 0,0 (see footnote, p. 370); that is, by the departure of the curved line cod from the

straight line cod.



FIG. 418. Reflection of a plane wave from a

convex mirror

Since 0,0 was made equal to 00, we

have 0,0,= 200; that is, the curvature

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wave is equal to twice the curvature of the mirror, or

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447. Image of an object in a convex mirror. We are all familiar with the fact that a convex mirror always forms behind the mirror a virtual, erect, and diminished image. The reason for this is shown clearly in Fig. 419. The image of the point P lies, ast in plane mirrors (see § 444), always on the perpendicular to the mirror, but now neces

FIG. 419

sarily nearer to the mirror than the focus F, since, as the point P is moved from a position very close to the mirror, where

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The moving-picture camera makes a series of snapshots upon a film, usually at the rate of 16 per second. The film is drawn past the lens with a jerky movement, being held at rest during the instant of exposure and moved forward while the shutter is closed. The pictures are -inch high and 1 inch wide. Since 1 foot of film per second is drawn past the lens, a recl of film 1000 feet long (the usual length) contains 16,000 pictures. From the rcel of negatives a reel of positives is printed for use in the projection apparatus. The optical illusion of "moving" pictures is made possible by a peculiarity of the eye called persistence of vision. To illustrate this let a firebrand be rapidly whirled in a circle. The spot of light appears drawn into a luminous arc. This phenomenon is due to the fact that we continue to see an object for a small fraction of a second after the image of it disappears from the retina. The period of time varies somewhat with different individuals. The so-called "moving" pictures do not move at all. In normal projection 16 brilliant stationary pictures per second appear in succession upon the screen, and during the interval between the pictures the screen is perfectly dark. It is during this period of darkness that the film is jerked forward to get the next picture into position for projection. The eye, however, detects no period of darkness, for on account of persistence of vision it continues to see the stationary picture not only during this period of darkness but dimly for an instant even after the next picture appears upon the screen. This causes the successive stationary pictures, which differ but slightly, to blend smoothly into each other and thus give the effect of actual motion

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1. A spherical sound wave. 2. The same wave .00007 second later. 3. A wave reflected from a plane surface, curvature unchanged. 4. A wave reflected from a convex surface, curvature increased. 5. The source at the focus of a SO, lens. The photograph shows first, the original wave on the right; second, the reflected wave, with its increased curvature; and third, the transmitted plane wave. 6. Source at focus of a concave mirror; the reflected wave is plane. (Taken by Professor A. L. Foley and Wilmer H. Souder, of the University of Indiana)

its image is just behind it, out to an infinite distance, its image moves back only to the focal plane through F. Hence the image must lie somewhere between F and the mirror. The image P'Q' of an object PQ is always diminished, because it lies between the converging lines PC and QC. It can be located by the ray method (Fig. 419) exactly as in the case of concave lenses. In fact, a convex mirror and a concave lens have exactly the same optical properties. This is because each always increases the curvature of the incident

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448. Images in concave mirrors. Let the images obtainable with a concave mirror be studied precisely as were those obtainable from a convex lens. It will be found that exactly the same series of images is obtained: when the object is between the mirror and the principal focus, the image is virtual,, enlarged, and erect; when it is at the focus the reflected waves are plane, that is, the rays from each point are a parallel bundle; when it is between the

FIG. 420. Real image of candle formed by a concave mirror


FIG. 421. Method of formation of a real image by a concave mirror

principal focus and the center of curvature, the image is inverted, enlarged, and real (Figs. 420 and 421); when it is at a distance R (= oC) from the mirror, the image is also at a distance R and of the same size as the object, though inverted; when the object is moved from R out to

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