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Illustration of a convex polyhedral angle. "The sum of the face angles of any convex polyhedral angle is less than four right angles."

Convex Polyhedral Angle

Illustration of a convex polyhedral angle. "The sum of the face angles of any convex polyhedral angle…

"The photographer's camera corresponds to the camera-obscura. A darkened box, adjustable in length, takes the place of the darkened room, and an achromatic convex lens is substituted for the aperture in the shutter." — Avery, 1895

Bellows Camera

"The photographer's camera corresponds to the camera-obscura. A darkened box, adjustable in length,…

"A modification of the simple kaleidoscope was introduced by Sir David Brewster, whereby the images of large and distant objects can be introduced into the picture. This is effected by removing the object box and replacing it by a tube carrying at its outer end a double convex lens, represented by LL. By a screw adjustment the lens can be so placed as to focus the distant object exactly in the plane of the sector AOB, and so bring its image into the very best position for producing symmetrical patterns. When this instrument is directed towards a tree in full bloom, a very beautiful effect is produced, which can be varied by gradually moving the instrument. This form was called by Brewster the telescopic kaleidoscope." —The Encyclopedia Britannica, 1910

Convex Lens

"A modification of the simple kaleidoscope was introduced by Sir David Brewster, whereby the images…

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

"Throw a sunbeam through a very small opening in the shutter of a darkened room. Receive the beam upon a convex lens of short focal length, placing a pieve of red glass between the aperture and the lens. Place and opaque screen with a sharp edge beyond the focal distance of the lens, as at a, so as to cut off the lower part of the cone of homogeneous light, and project the upper part thereof upon a screen at b." -Avery 1895

Diffraction

"Throw a sunbeam through a very small opening in the shutter of a darkened room. Receive the beam upon…

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Irregular Convex Dodecagon

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Irregular Convex Dodecagon

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Irregular Convex Dodecagon

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

"If the cornea is too convex, or prominent, the image will be formed before it reaches the retina, for the same reason, that of two lenses, that which is most convex will have the least focal distance." -Comstock 1850

Cornea too Convex on Eye

"If the cornea is too convex, or prominent, the image will be formed before it reaches the retina, for…

A magnifying glass.

Magnifying Glass

A magnifying glass.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon.

Illustration of an irregular convex hexagon.

Irregular Convex Hexagon

Illustration of an irregular convex hexagon.

Illustration of an irregular convex hexagon with symmetry.

Irregular Convex Hexagon

Illustration of an irregular convex hexagon with symmetry.

"If the object a be placed obliquely before the convex mirror, then the converging rays from its two extremities falling obliquely on its surface, would they prolonged through the mirror, meet at the point c, behind it. But instead of being thus continued, they are thrown back by the mirror in less convergent lines, which meet the eye at e, it being, as we have seen, one of the properties of this mirror, to reflect converging rays less convergent than before." -Comstock 1850

Curved Image

"If the object a be placed obliquely before the convex mirror, then the converging rays from its two…

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved and the other plane.(1) Double convex(2) Plano convex(3) Meniscus(4)Double concave(5) Plano concave(6) Concavo concave." -Avery 1895

Lens

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved…

"A double convex lens of crown-glass may be combined with a plano-convex lens of flint-glass so as to overcome the dispersive effect for some of the colors without overcoming the converging effect." -Avery 1895

Achromatic Lens

"A double convex lens of crown-glass may be combined with a plano-convex lens of flint-glass so as to…

"The shape of the double convex lens, d, c, is that of two plano-convex lenses, placed with their plane surfaces in contact, and consequently the focal distance of this lens is nearly the centre of the sphere of which one of its surfaces is a part." -Comstock 1850

Double Convex Lens

"The shape of the double convex lens, d, c, is that of two plano-convex lenses, placed with their plane…

"Double convex lenses are used in the eyeglasses for old people, becoming more spherical according to the age of the person or the magnifing power required." -Comstock 1850

Double Convex Lens Magnifing an Arrow

"Double convex lenses are used in the eyeglasses for old people, becoming more spherical according to…

"The double convex lens may be described as the part common to two spheres that intersect each other. The centers of the limiting spherical surfaces, as c and C, are the centers of curvature. The straight line, XY, passing through the centers of curvature is the principal axis of the lens." -Avery 1895

Double Convex Lens

"The double convex lens may be described as the part common to two spheres that intersect each other.…

"Thus the pencils of converging rays, are rendered still more convergent by their passage through the lens, and are therefore brought to a focus nearer the lens, in proportion to their previous convergency." -Comstock 1850

Converging Rays and a Double Convex Lens

"Thus the pencils of converging rays, are rendered still more convergent by their passage through the…

"If diverging rays fall on the surface of the same lens, they will, by refraction, be rendered less divergent, parallel, or convergent, according to the degrees of their divergency, and the convexity of the surface of the lens." -Comstock 1850

Diverging Rays from a Double Convex Lens

"If diverging rays fall on the surface of the same lens, they will, by refraction, be rendered less…

"If the whole circle be considered the circumfrence of a sphere, of which the plano-convex lens b, a, is a section, then the focus of parallel rays, or the principal focus, will be at the opposite side of the sphere, or at c." -Comstock 1850

Plano Convex Lens

"If the whole circle be considered the circumfrence of a sphere, of which the plano-convex lens b, a,…

"View of an arrow through a plano convex lens will have the arrow appear smaller than it actually is." -Comstock 1850

View of an Arrow Through a Plano Convex Lens

"View of an arrow through a plano convex lens will have the arrow appear smaller than it actually is."…

"Let a candle c, be placed on the inside of a box or tube, so that its light may pass through the plano-convex lens n, and strongly illuminate the object o. This object is generally a small transparent painting on a slip of glass, which slides through an opening in the tube. In order to show the figures in the erect position, these paintings are inverted, since their shadows are again inverted by the refraction of the convex lens m." —Comstock, 1850

Magic Lantern

"Let a candle c, be placed on the inside of a box or tube, so that its light may pass through the plano-convex…

An illustration of the convex of a meniscus.

Convex of Meniscus

An illustration of the convex of a meniscus.

"This consists of two convex lenses, by one of which the image is formed within the tube of the instrument, and by the other this image is magnified as seen by the eye; so that by this instrument the object itself is not seen, as with the single microscope, bu we see only its magnified image." -Comstock 1850

Compound Microscope

"This consists of two convex lenses, by one of which the image is formed within the tube of the instrument,…

"This consists of two lenses, one of which is called the condesner, because it is employed to concentrate the rays of the sun...The other is a double convex lens, of considerable magnifing power, by which the image is magnified." -Comstock 1850

Solar Microscope

"This consists of two lenses, one of which is called the condesner, because it is employed to concentrate…

"When the rays diverge from a point beyond the center of curvature, as B, the focus falls on the same axis, at a distrance from the mirror greater than that of the principal focus, and less than that of the center of curvature." -Avery 1895

Rays Diverging from Beyond the Center of Curvature on a Concave Mirror

"When the rays diverge from a point beyond the center of curvature, as B, the focus falls on the same…

"A convex mirror is a part of a sphere, or globe, reflecting from the outside." -Comstock 1850

Convex Mirror

"A convex mirror is a part of a sphere, or globe, reflecting from the outside." -Comstock 1850

"Hence the image of the object, when reflected from the convex mirror, appears smaller than the object itself." -Comstock 1850

Object Diminished in Convex Mirror

"Hence the image of the object, when reflected from the convex mirror, appears smaller than the object…

"To explain this, let us suppose that the arrow a, is diminished by reflection from the convex surface, so that its image appearing a d, with the eye at c, shall seem as much smaller in proportion to the object, as d is less than a. Now keeping the eye at the same distance from the mirror, withdraw the object, so that it shall be equally distant with the eye, and the image will gradually diminish, as the arrow is removed." -Comstock 1850

Convex Mirror

"To explain this, let us suppose that the arrow a, is diminished by reflection from the convex surface,…

"...as the arrow is moved backwards, the angle at c, must be diminished, because the rays flowing from the extremities of the object fall a greater distance before the reach the surface of the mirror; and as the angles of the reflected rays bear a proportion to those of the incident ones, so the angle of vision will become less in proportion, as the object is withdrawn." -Comstock 1850

Convex Mirror

"...as the arrow is moved backwards, the angle at c, must be diminished, because the rays flowing from…

"Let us suppose that a, is a luminous point, from which a pencil of diverging rays falls upon a convex mirror. These rays, as already demonstrated, will be reflected more divergent, and consequently will meet the eye at e, in a wider state of dispersion that they fell upon the mirror at o." -Comstock 1850

Convex Mirror

"Let us suppose that a, is a luminous point, from which a pencil of diverging rays falls upon a convex…

"A convex mirror is generally a part of the other surface of a spherical shell. It increases the divergence, or decreases the convergence of light that falls upon it. The foci are virtual; the principal focus is midway between the center of the mirror and the center of curvature. The foci may be located and the images determined by processes closely similar to those used for concave mirrors, as illustrated." -Avery 1895

Convex Mirror

"A convex mirror is generally a part of the other surface of a spherical shell. It increases the divergence,…

"Rays from an object showing the reproduction of an image in a convex mirror." -Avery 1895

Convex Mirror Reproducing an Image of an Arrow

"Rays from an object showing the reproduction of an image in a convex mirror." -Avery 1895

"A convex mirror reflects from a curved surface rounding out like the outside of an orange." —Quackenbos 1859

Convex Mirror

"A convex mirror reflects from a curved surface rounding out like the outside of an orange." —Quackenbos…

"Parallel rays strike the convex mirror, reflect, and diverge as if they had originated from a virtual focus inside the mirror. Focus F is located between the surface of the mirror and the mirror's center if it were a full body sphere." —Quackenbos 1859

Reflection by Convex Mirrors

"Parallel rays strike the convex mirror, reflect, and diverge as if they had originated from a virtual…

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Convex Nonagon

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9…

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Convex Nonagon

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9…

Illustration of a regular nonagon. A nonagon is a closed geometric figure with 9 sides. A regular nonagon has 9 equal sides and 9 equal angles.

Regular Nonagon

Illustration of a regular nonagon. A nonagon is a closed geometric figure with 9 sides. A regular nonagon…

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon.

Irregular Convex Octagon

Illustration of an irregular convex octagon.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Irregular Convex Pentagon

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Irregular Convex Pentagon

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Illustration of an irregular convex pentagon.

Irregular Convex Pentagon

Illustration of an irregular convex pentagon.

"Another form is called the polyangular kaleidoscope. The only essential difference in it is that the mirrors are so arranged that the angle between them can be varied at pleasure. This, being very useful for illustrating the theory of the instrument, is the form usually found in collections of philosophical apparatus." —The Encyclopedia Britannica, 1910

Polyangular Kaleidoscope

"Another form is called the polyangular kaleidoscope. The only essential difference in it is that the…

Illustration of a convex polygon. A polygon is convex when no side when produced will enter the polygon.

Convex Polygon

Illustration of a convex polygon. A polygon is convex when no side when produced will enter the polygon.

Illustration of an irregular convex polygon with 16 sides that has symmetry. It could be used to show rotation of a square.

Irregular Convex Polygon

Illustration of an irregular convex polygon with 16 sides that has symmetry. It could be used to show…

"Fill with carbon dioxide a large rubber toy balloon or other double-convex lens having easily flexible walls. Suspend a watch, and place yourself so that you can just hear its ticking. Have the gas-filled lens moved back and forth in the line between watch and and ear until the ticking is much more plainly heard. Use a glass funnel as an ear-trumpet." -Avery 1895

Sound Refraction

"Fill with carbon dioxide a large rubber toy balloon or other double-convex lens having easily flexible…