Rays are lines on a diagram ... like the equator on a map. Rays show the direction of wave motion (propagation) - nothing more. Rays are not real they are just construction lines to aid understanding.
Two rays are shown in the upper diagram. They come from the tip of the object, pass through the convex lens and intersect again at the tip of the image. These same two rays - one parallel to the axis, bending to pass through the focal point, the other to the center, passing straight through - are useful (with minor changes) for all thin lenses and mirrors. Light enters the eye shown as thought it came from the image. The image is seen 'floating' in space between the lens and the viewer.
Light energy is concentrated at the image. Loosely speaking, the image shown in the upper diagram is hot.
Moving the object both moves and changes the size of the image. If the object is outside two focal lengths the image is reduced. If it is between one and two focal lengths the image is enlarged.
The same two rays from the tip of the object pass through the lens in the lower diagram at right They do not intersect. There is no concentration of energy and no "hot" image. Instead the rays appear to have come from a point behind the lens. The image is behind the lens. We can see the image but there is no concentrated light energy. The virtual image in a magnifying glass is cold.
Moving the object closer to the focal length increases the magnification.
Hot and cold are good descriptions but they are not the words used in the books. Physics types say real and virtual without stopping to think about it.
Remember; a real image is hot; a virtual image is cold. A real image can be seen on a screen. A virtual image cannot be projected on a screen, otherwise they look the same.
Notes:
1 The same convex lens can be used to burn holes in paper or to make a magnifying glass. Both effects can be explained with ray diagrams.
2 A virtual image is sometimes called imaginary. The description is not strictly speaking correct. The image is not in your imagination - it is there, you do see it.
3 The real image described above is known as the primary image and the focal point as the primary focus. A lens forms secondary images due to partial reflections from the curved surfaces. It is an interesting exercise to look for the series of secondary images formed by a large thin convex lens, with a small strip of white card, using a bright filament as an image.
Comparisons are often more instructive than absolute values. In this exercise a student is asked to compare and contrast the appearance and the positions of the two reflections made by the two surfaces of a glass lens.
1 Find an overhead light. Hold a large convex lens at arms length. Tilt it, look into it, study the bright reflections of the light. Thee are two. [If you see four reflections your eyes are not working together to focus on the reflections - be patient - the four will become two if you wait].
2 Focus your attention on the smaller reflection. Use both eyes, look carefully. Where is the image? Allow a moment for your eyes to work together. The image is floating in space, above the lens.
3 Take a pencil. Carefully bring the pencil across to the image. Where exactly is it (to the nearest mm)? Stereopsis is the ability to see in three dimensions by combining two views from different places (on either side of your nose). You are not looking at a hologram. You are looking at an a real image in space, between you and the glass.
4 Switch your attention to the larger of the two reflections. Use the same patient technique. Where is it? Floating also, but this time below the glass.
The small upper image is formed by two refractions at the upper surface and a partial reflection from the lower concave surface. The larger lower image is formed by a single partial reflection from the upper convex surface. The reflections of a candle flame in a wine glass are not on the glass. They are inside or outside - try it some time.
5 Try the same thing with a range of spectacle lenses. Describe the various combinations and relate the image positions to the curvature of each surface.
1 Povray
Patterns of light on the bottom of a swimming pool - beautiful yes - accidental no. Plays of light and shade, of color and highlight are the direct result of the placement and nature of the light source and the bending and bouncing of light waves encountering objects both transparent and reflective. The illustration at right is not a photograph. It is a computer display created by a ray diagram calculation in a program called POVRAY. The ray diagram calculation has been rendered to represent what is actually seen.
Excellent commercial applications exist. The lights on the bridges over the Seine in Paris were designed in virtual reality first. When the engineers had decided on the look they wanted they put in the lights, saving millions of dollars and doing the job right first time.
2 Halo simulations
Cowley and Schroeder have done extensive work developing a ray tracing halo simulation program which is available for PC on the web. Running their color simulation with one million rays, for hexagonal ice crystals with a long axis:diameter ratio of 2 and horizontal orientation within ±2° gives a 22° halo which is essentially identical to an intense 22° halo photographed at ISB on May 25th 2000. Detailed images of the simulation and the actual halo show the same color structure.
A similar but more diffuse halo photographed on August 17th 2000 was less well defined with a red to yellow inner ring and a broad outer white area. Simulating a halo with 20 million rays and short (a/d = 1.2) hexagonal crystals with random orientation gives a similar halo. The simulation has been blurred slightly to remove the pixelation and pasted as a 50% layer to a cloud background.
The bright halo is formed at minimum deviation. Note the apparently darked interior, since rays are refracted at greater angles from the outside.