Lab Activity: Plane and Spherical Mirrors
In this lab you will use ray tracing to determine the images produced by plane and spherical mirrors. You will use the mirror equation to determine the position of the image as well as the type of image and compare that with actual measurements you make. The mirror equation will be derived in lecture.
Part 1: Plane mirrors and ray diagrams
1. Place the mirror vertically (upright) in the center of your paper and trace out the front and back surfaces of the mirror on the paper. With the mirror still on the paper, being careful not to move the mirror, place a very small object in front of the mirror. Trace the position of the object on the paper.
2. Take a look at the image in the image in the mirror. Where do you think the image is? Is it: in front of, behind, or on the surface of the mirror? Can you think of a way to show that your hypothesis is correct?
3. Everyone grab a meterstick. Each person should line up their meterstick along their line of sight to the image in the mirror (point to the image with one end of the stick while putting your eye up next to the other end of the meterstick). Make sure that each of you point to the same place on the object! Where do all the metersticks point? Do all of your metersticks point to a single location? This location is where the image is. Was your hypothesis in 2 correct?
4. Now, one person at a time, place your meter stick on the table and get down so that your eye is level with the table top. With your eye down next to the meterstick, line the edge of the meterstick up with the image in the mirror. Without moving your meterstick, carefully trace along the edge of your meterstick on your piece of paper. You should have at least 4 lines drawn in on your paper (you will have to draw several lines each). Be very careful and precise while completing this step.
5. Remove the object and the mirror from the paper. Continue the lines by drawing on the paper to the place where the lines converge. This would be the location of the “image”. How far away from the mirror is the image?
6. In order for you to see the image in the mirror, light has to enter your eye. Did the light entering your eye really come from the location of the image itself? Where does the light entering your eye really come from?
7. Here are a few definitions…
A ray is the line along which the light travels (or path of the light).
A ray which strikes the surface of the mirror is said to be incident.
The angle between the incident ray and the normal to the mirror is called the angle of incidence.
The angle between the reflected ray and the normal to the mirror is called the angle of reflection.
The law of reflection states that the angle of incidence is equal to the angle of reflection.
Using this information, construct the incident rays. Where do these lines intersect?
8. What you have just completed is a “ray diagram” for a plane mirror. The kind of image produced by a plane mirror is what we call a virtual image. Since the light that enters our eyes really does not originate at the image itself, the image is considered to be virtual. Other kinds of mirrors can produce a real image. If the light had come directly from the image (like a movie on a screen where light is reflected off of a screen and into your eye) it would be called a real image. See your instructor to see a curved mirror that can create a real image.
Part 2: The Method of Parallax and Locating Images
The Method of Parallax:
A. Close one eye and lean down in your chair so that your open eye is at table level. Next, have your partner drop a very small piece of paper (about 2mm square) onto the table.
Hold one finger above the table and then move your finger until you think it is directly above the piece of paper. Move your finger straight down to the table and check whether your finger actually is in fact directly above the paper.
Try this exercise several times, with your partner dropping the piece of paper at different locations each time. Keep your open eye at table level. After several tries, exchange roles with your partner.
How can you account for the fact that when your finger misses the piece of paper, your finger is always either in front of or behind the paper, but never to the left or right of it?
B. Suppose that you placed your finger behind the paper (as shown below) while trying to locate the piece of paper.
Predict whether your finger would appear to be located to the left of, to the right of, or in line with the piece of paper if:
· You move your head left
· You move your head right
Check your predictions and resolve any inconsistencies.
C. Suppose you had placed your finger in front of the piece of paper rather than behind it. Predict whether the paper or your finger would appear on the left when you move your head to the left. Check your answer experimentally.
D. Devise a method based on your results from parts B and C by which you could locate the piece of paper. Your method should include how to tell whether your finger is directly over the paper and, if not, whether it is in front of or behind the piece of paper. Describe your method to your partner and then test your method.
E. Check your method with your instructor.
The method that you have developed for locating the piece of paper is called the method of parallax.
Image Location Using the Parallax Method:
Obtain a small mirror and a nail. Place the mirror in the middle of a sheet of paper. Stand the nail on its head about 10 cm in front of the mirror. We will call this nail the object.
On your paper, mark the locations of the mirror and the nail.
A. Place your head so that you can see the image of the nail in the mirror. Use the method of parallax to position your pencil so that it is located in the same place as the image of the nail in the mirror.
Would observers at other locations agree that the image is located at the place you marked? Check your answers experimentally.
B. Move the nail off to the right side of the mirror (about 5cm from the nearest edge of the mirror). Find the new image location.
Where must your head be in order to observe the image of the nail?
Complete a ray diagram which illustrates the positions from which you are able to view the image of the nail.
Report
Complete part 1 on this handout by turning in a clean, clear, and complete ray tracing diagram with notes that show your work. Make sure your handwriting is legible. Use a ruler for diagrams. There will be deductions if your work is not clean enough.
Do end-of chapter problems 7, 39 and 77. Show your work.
Spherical Mirrors
You can use any two rays starting on some point on the object and hitting the reflecting or refracting surface to help you find the image produced. However, for spherical mirrors and lenses there are three incident rays that are easier to draw than others and that we will therefore use for ray tracing. These rays are called principal rays:
1. A ray parallel to the principal axis.
2. A ray through the focal point.
3. A ray through the center of curvature (mirror) or through the optical center (thin lens).
The principal rays are reflected/refracted differently depending on whether the reflecting/refracting object is a convex/concave mirror or lens.
Ray Diagrams for Spherical Mirrors
The three principal rays for converging (concave) mirrors:
1. Any incident ray parallel to the principal axis is reflected through the focal point (which is located at ½ R where R is the distance from the mirrors center (or vertex) to the center of curvature C.
2. Any incident ray which passes through the focal point is reflected parallel to the principal axis.
3. Any incident ray which passes through the mirror’s center of curvature C (i.e. along the radius) is reflected back upon itself.
The three principal rays for diverging (convex) mirrors:
1. Any incident ray parallel to the principal axis is reflected as if it came from the focal point (which is located at ½ R behind the mirror’s surface where R is the distance from the mirror’s center (or vertex) to the center of curvature C.
2. Any incident ray which is directed towards the focal point is reflected parallel to the principal axis.
3. Any incident ray directed towards the mirror’s center of curvature C (i.e. along the radius) is reflected back upon itself.
Practice drawing ray diagrams: Finish the ray diagrams for the following concave and convex mirror setups using the rules for diagramming as given above. Do this for
a) an object located between C and F
b) an object located beyond C
c) an object located between V and F
for the concave mirror and the case given for the convex mirror.
Questions:
For each case give your answers to the following questions in the table below:
1. Is the image larger or smaller than the object?
2. Is the image upright or inverted?
3. Is the image real or virtual?
Mirror / Object location / Image location / Image larger/smaller / Image upright/inverted / Image real/virtual / Exp. CheckConcave / between
C & F (case a)
beyond C
(case b)
between
V & F (case c)
Convex / in front of mirror J
A shaving mirror would be an example of a convex or a concave mirror? Where would you put your face?
The spherical mirror on a car’s side mirror would be an example of a convex or concave mirror. Explain the warning: “Vehicles in mirror are closer than they appear!”
Ask your instructor to show you the experimental setup for mirrors and check your findings experimentally (check box in table when you are satisfied).
Quantitative:
/How to find
/concave mirror, object between C&F
/concave mirror, object beyond C
/concave mirror, object between V&F
/convex mirror
object distance d0 (measured)
/ruler
/ / / /image distance di (measured)
/ruler
/ / / /focal length f (measured)
/ruler
/ / / /object size h0 (measured)
/ruler
/ / / /image size hi (measured)
/ruler
/ / / /magnification M (measured)
/M=hi/ho
/ / / /image distance di (calculated)
/di=dof/(do-f)
/ / / /magnification M (calculated)
/M=-di/do
/ / / /image size hi (calculated)
/hi= M ho
/ / / /from diagram, image larger/smaller?
/ / / / /from calculation, image larger/smaller?
/ / / / /from diagram, image upright/inverted?
/ / / / /from calculation, image upright/inverted?
/ / / / /from diagram, image real/virtual?
/ / / / /from calculation, image real/virtual?
/ / / / /Make sure everything makes sense! Calculations and ray tracing results should be in agreement. All of the sign conventions are given at the end of this tutorial.Equations:
Mirror Equation
Sign Conventions
The mirror equation and the thin lens equation work for both convex and concave mirrors and lenses if you use the correct sign conventions.
Mirrors
Quantity / Positive when / Negative whenObject location do / object is in front of mirror (real object) / object is in back of mirror (virtual object)
Image location di / image is in front of mirror (real image) / image is in back of mirror (virtual image)
Image height hi / image is upright / image is inverted
Focal length f and radius R / mirror is concave / mirror is convex
Magnification M / image is upright / image is inverted
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