Prismslight

A right prism is a prism in which the top and bottom polygons lie on top of each other so that the vertical polygons connecting their sides are not only parallelograms, but rectangles (right figure). A prism that is not a right prism is known as an oblique prism. If, in addition, the upper and lower bases are rectangles, then the prism is known as a cuboid.

Prismsmath

A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure).

50 through 57 55, 57 53 Thin lenses. Object Ostands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance localid="1662982946717" iand (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V) , (d) inverted (I) from object O or non inverted (NI), and (e) on the same side of the lens as object Oor on the opposite side.

Prismsmeaning

Figure 34-27 is an overhead view of a mirror maze based on floor sections that are equilateral triangles. Every wall within the maze is mirrored. If you stand at entrance x, (a) which of the maze monsters a, b, and chiding in the maze can you see along the virtual hallways extending from entrance x; (b) how many times does each visible monster appear in a hallway; and (c) what is at the far end of a hallway?

The regular right prisms have particularly simple nets, given by two oppositely-oriented -gonal bases connected by a ribbon of squares. The graph corresponding to the skeleton of a prism is known, not surprisingly, as a prism graph.

Types ofprisms

A double-convex lens is to be made of glass with an index of refraction of 1.5.One surface is to have twice the radius of curvature of the other and the focal length is to be 60mm. What is the (a) smaller and (b) larger radius?

The above figure shows the first few regular right prisms, whose faces are regular -gons. The 4-prism with unit edge lengths is simply the cube. The dual polyhedron of a regular right prism is a dipyramid.

Prismsshapes

Since one surface has twice the radius of the other and since one surface is convex to the incoming light while the other is concave, we can write,

PrismsVR

The algebraic degrees of these areas for , 4, ... are 2, 1, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 8, 4, 16, 6, 18, 4, ... (OEIS A089929).

An object is placed against the center of a thin lens and then moved away from it along the central axis as the image distance is measured. Figure 34-41 gives i versus object distance p out to ps=60cm. What is the image distancewhen p=100cm?

A corner reflector, much used in the optical, microwave, and other applications, consists of three plane mirrors fastened together to form the corner of a cube. Show that after three reflections, an incident ray is returned with its direction exactly reversed.

The regular right equilateral prisms are canonical polyhedra whose duals are canonical dipyramids. Canonical prisms have midradius equal to the circumradius of their -gonal faces, i.e.,

An object is placed against the center of a converging lens and then moved along the central axis until it is 5.0mfrom the lens. During the motion, the distance between the lens and the image it produces is measured. The procedure is then repeated with a diverging lens. Which of the curves in Fig. 34-28 best gives versus the object distance p for these lenses? (Curve 1 consists of two segments. Curve 3 is straight.)