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Diverging lens

A lens that causes the light rays to bend away from its axis is called a diverging lens.

As noted in the initial discussion of the law of refraction in The Law of Refraction , the paths of light rays are exactly reversible. This means that the direction of the arrows could be reversed for all of the rays in [link] and [link] . For example, if a point light source is placed at the focal point of a convex lens, as shown in [link] , parallel light rays emerge from the other side.

Three light rays coming from a light bulb filament are incident on a convex lens and the rays after refraction are rendered parallel.
A small light source, like a light bulb filament, placed at the focal point of a convex lens, results in parallel rays of light emerging from the other side. The paths are exactly the reverse of those shown in [link] . This technique is used in lighthouses and sometimes in traffic lights to produce a directional beam of light from a source that emits light in all directions.

Ray tracing and thin lenses

Ray tracing is the technique of determining or following (tracing) the paths that light rays take. For rays passing through matter, the law of refraction is used to trace the paths. Here we use ray tracing to help us understand the action of lenses in situations ranging from forming images on film to magnifying small print to correcting nearsightedness. While ray tracing for complicated lenses, such as those found in sophisticated cameras, may require computer techniques, there is a set of simple rules for tracing rays through thin lenses. A thin lens is defined to be one whose thickness allows rays to refract, as illustrated in [link] , but does not allow properties such as dispersion and aberrations. An ideal thin lens has two refracting surfaces but the lens is thin enough to assume that light rays bend only once. A thin symmetrical lens has two focal points, one on either side and both at the same distance from the lens. (See [link] .) Another important characteristic of a thin lens is that light rays through its center are deflected by a negligible amount, as seen in [link] .

Thin lens

A thin lens is defined to be one whose thickness allows rays to refract but does not allow properties such as dispersion and aberrations.

Take-home experiment: a visit to the optician

Look through your eyeglasses (or those of a friend) backward and forward and comment on whether they act like thin lenses.

Figure (a) shows three parallel rays incident on the right side of a convex lens; after refraction they converge at F on the left side of the lens. The distance from the center of the lens to F is small f. Figure (b) shows three parallel rays incident on the right side of a concave lens; after refraction they appear to have come from F on the right side of the lens. The distance from the center of the lens to F is small f.
Thin lenses have the same focal length on either side. (a) Parallel light rays entering a converging lens from the right cross at its focal point on the left. (b) Parallel light rays entering a diverging lens from the right seem to come from the focal point on the right.
Figure (a) shows a light ray passing through the center of a convex lens without any deviation. Figure (b) shows a light ray passing through the center of a concave lens go without any deviation.
The light ray through the center of a thin lens is deflected by a negligible amount and is assumed to emerge parallel to its original path (shown as a shaded line).

Using paper, pencil, and a straight edge, ray tracing can accurately describe the operation of a lens. The rules for ray tracing for thin lenses are based on the illustrations already discussed:

  1. A ray entering a converging lens parallel to its axis passes through the focal point F of the lens on the other side. (See rays 1 and 3 in [link] .)
  2. A ray entering a diverging lens parallel to its axis seems to come from the focal point F. (See rays 1 and 3 in [link] .)
  3. A ray passing through the center of either a converging or a diverging lens does not change direction. (See [link] , and see ray 2 in [link] and [link] .)
  4. A ray entering a converging lens through its focal point exits parallel to its axis. (The reverse of rays 1 and 3 in [link] .)
  5. A ray that enters a diverging lens by heading toward the focal point on the opposite side exits parallel to the axis. (The reverse of rays 1 and 3 in [link] .)
Practice Key Terms 8

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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