Apparatus Competition

2006 AAPT Summer Meeting

Syracuse, NY

Light Ray Focusing Demonstrator

John W. Zwart

Dordt College

Department of Physics

498 4^th Ave NE

Sioux Center, IA 51250

712-722-6288

zwart ‘at’ dordt ‘dot’ edu

Abstract:

Many students struggle to make the connection between image formation with a converging lens and 2-D ray tracing methods in which two or three rays from a single object point are used to find the image. This demonstration builds an ‘object’ from individually switched small lights which act as near point sources. The cone of light produced by the lens from one point on the object can be shown using a translucent screen by moving it from the lens to the focus point and beyond. The image can then be built up point by point.

Construction of Apparatus:

The apparatus, minus mounting ring stands, is shown below in Figure 1. The imaging screen consists of a sheet of tracing paper taped to an overhead transparency frame. The one item that requires addition construction is the box containing the six miniature clear Christmas tree lights and switches.

(a) (b)

Figure 1. (a) Demonstration apparatus purchased or constructed items. (b) Reverse side of light box showing switches, power input jack, and separate power supply.

A project box is used to make the light box. The mounting rod is a five inch long, 3/8” diameter carriage bolt attached through a hole drilled in the side of the box. The bolt head was cut off and the rod end filed to make mounting easier. Six lights and sockets were cut from the fifty light miniature string of clear Christmas tree lights, leaving 46 replacement bulbs. Each individual light requires 2.5-3.0 V. Holes were drilled in the project box to form an arrow pattern and the sockets force fit into the holes. A set of switches is mounted in the lid of the project box in the same pattern. Each bulb was connected to its corresponding switch and the lights with switches were connected in parallel to the 3.0 V input socket. Thus, each light can be independently turned on or off.

The power supply is a selectable voltage AC adapter. At 3.0 V, each bulb draw 140 mA, so the supply needs to be capable of supplying nearly 900 mA when all lights are on.

A very ‘quick and dirty’ implementation of this demonstration can be done by using an intact string of lights and the lid of a paper carton. See Figure 3. A few weights are placed in the base of the lid to hold it upright. Holes are punched in the face of the carton, and one or more lights are pushed through the holes. The rest of the lit up string is hidden behind the lid. While this does offer ease of construction, one drawback is that frequently a bulb comes loose while inserting the string which shuts off all of this series set of bulbs. It can be a time sink to search for the loose bulb.

Figure 3. Boxtop light source

Figure 2. Apparatus mounted for demonstrations.

Use of Apparatus:

This demonstration is best performed in a darkened room.

The apparatus is set up as shown in Figure 2. However, it is easier to handhold the screen than to leave it mounted as shown in the figure. In a classroom setting, the lights and lens should face the class. For the lens used, a light-lens separation of 55 cm or so is a good starting distance. Holding the screen directly in front of the lens shows a circle of light. Moving it further away from the lens shows the circle decreasing in diameter and increasing in brightness until the focus location is reached and then the light spreads out again, See Figure 4.

Figure 3. Boxtop light source

Figure 4. Two slices of the cone of light for a single light source.

The process described above can be repeated with two adjacent lights switched on. As the screen is moved away from the lens, the separate sources of light become distinguishable.

Finally, with the screen at the focused image location, each light can be turned on one at a time, establishing that each point on the object corresponds to a point in the image, as shown below in Figure 5. The process can be repeated with other lights – lens separation distances. If the lens is closer to the lights than its focal length, the rays can be shown to diverge.

Figure 5. Complete image.