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The figure on the top shows an expanded view of refraction for ray 1 falling on a concave lens. The angle of incidence is theta 1 and angle of refraction theta 2. The ray after the refraction at the second surface emerges with an angle equal to theta 1 prime with the perpendicular drawn at that point. Perpendiculars are shown as dotted lines. The figure at the bottom shows a concave lens. Three rays, 1, 2, and 3, are considered. Ray 2 falls on the axis and rays 1 and 3 are parallel to the axis. Rays 1 and 3 after refraction appear to come from a point F on the axis. The distance from the center of the lens to F is small f and is measured from the same side as the incident rays. Ray 2 on the axis goes undeviated.
Rays of light entering a diverging lens parallel to its axis are diverged, and all appear to originate at its focal point F size 12{F} {} . The dashed lines are not rays—they indicate the directions from which the rays appear to come. The focal length f size 12{f} {} of a diverging lens is negative. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.

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).

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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