Improving Your Image Lab
Resource Downloads
The Following Information is Provided to the Student
Question: What is the mathematical relationship between the number of images formed by a combination of two plane mirrors and the angle between the mirrors?
Purpose: To determine the mathematical equation which relates the number of images (N) formed by a set of two plane mirrors to the angle (θ) between the mirrors?
A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion. The Data section should include an organized table of labeled data (with unit), a graph of the number of images vs. the angle between mirror (with labeled axes) and some form of data analysis which leads to an appropriate conclusion. The data analysis could involve linear regression (with slope, y-intercept, regression constant and equation), power regression (with coefficients, power, regression constant and equation) or simply a trial-and-error process of equation fitting. Whatever method is used to link the data to an equation, the process should be fully documented.
Scoring Ruberic
| RM6. | Infinity Derivation | Score |
|---|---|---|
| _____ | Included, labeled and organized all parts of the lab report. | _____ / _____ |
| _____ | Data section includes diagram with two parallel mirrors, object and the several images to the left and to the right of the mirrors. Image distances are stated. The process used to determine the equation is documented and logical. A clear effort to derive an equation is documented; unsuccessful attempts may be shown and ruled ineffective. Logic and reasoning are evident; the final equation(s) is(are) consistent with distances stated in the diagram. Equation(s) is/are accurate and works; process of finding it is thoroughly documented. | |
| _____ | Conclusion states the equation or equations which relate(s) the distance between the nth image and the rightmost mirror in terms of pertinent variables; definition of variables is clearly stated. | |
| _____ | Discussion of Results shows how the equation can predict the first five image distances to the right of the right-most mirror. Work is shown and labeled. |
Lab Details
Materials Required
Two plane mirrors with a vertical mount; protractor; pencil or pen.
Description of Procedure
Two plane mirrors are used to create an adjustable angle mirror. The mirrors are placed in an upright position on the table with the meeting point of the two mirrors at the protractor's origin. The mirrors are arranged to make a 180° angle with each other. A pencil is placed in front of the mirrors and the number of images is counted. The process is repeated for a 90° angle, a 72° angle, 60° angle, etc. with a pencil placed between the mirrors and the number of images is counted. The process is continued for many more angles in order to determine the relationship between the number of images (N) and the angle (θ) between the mirrors. Once the data is collected, an equation is developed.
Safety Concerns
There is always a higher than usual level of risk associated with working in a science lab. Teachers should be aware of this and take the necessary precautions to insure that working environment is as safe as possible. Student horseplay (especially the use of meter sticks as swords) and off-task behaviors should not be tolerated.
Suggestions, Precautions, Notes
- Square mirrors a foot along their edge can be purchased at home stores and department stores. Two mirrors can be taped together along their edge with duct tape to form an adjustable angle mirror.
- Here are two methods for vertically mounting a plane mirror so that it stands upright on a sheet of paper. First, 1-inch-thick strips of wood with the same dimensions as the mirrors can be cut and glued to the back of the mirrors. The wood must be perfectly flat along one of its edges. Second, large binder clips could be purchased and clipped to the bottom sides of your mirrors to provide a base of support.
- Most inexpensive mirrors are coated with a reflective material on the back surface of a thin pane of glass. This does cause difficulties for many optics labs since the reflecting surface is actually behind the glass and not on the glass. A quick fix is to use a so-called two-way mirror which has its reflective coating on the front of the glass (actually, on both sides of the acrylic). An acrylic sheet can be purchased and cut into 3"x5" strips for a cost of approximately $2 per mirror. Avoid scratching the mirror during the cutting process.
- This lab offers students a challenging exercise in equation fitting. Students generally find the data collection process fun; they are thrilled to see so many images (especially for the really small angles). An equation which fits the data can often be found by inspection and careful analysis; students will have to experiment. Having the correct measurements will help - consider the results for the following strategic angles: 180°; 1; 90°:3; 72°:4; 60°:5; 45°:7; 40°:8; 30°:11; and 20°:17. Graphing the data also yields results (the relationship is inverse), though the results tend to be less meaningful.
Links
Connections to The Physics Classroom Tutorial:
The following reading is a suitable accompaniment to this lab:
http://www.physicsclassroom.com/Class/refln/u13l2f.cfm