Download Physics 221 – Lab 7 Spherical mirrors

Physics 221 – Lab 7
Spherical mirrors
The format for this lab and the next lab will be different from the previous labs. Print a copy of this lab
and fill in the information where requested. Your report will consist of the completed copy of the lab.
Each member of the lab group must complete their own copy -- all copies will be collected.
Procedure Materials and equipment: PASCO optics kit.
Consider a spherical mirror, that is, a mirror whose reflecting surface is a portion of a sphere. The
center of curvature, C, of the mirror is the center of the (imaginary) sphere of which the mirror is a part;
C lies on the Principal Axis which is a line perpendicular to the mirror's surface and is a distance R from
the mirror. R is called the radius of curvature of the mirror.
If light rays, originally parallel to the Principal Axis, strike a spherical concave mirror, they will reflect and
(to a close approximation) converge to the focal point, F.
1. In the space provided below, draw the situation just described; label C, R, F, and f (the focal length).
Draw your rays going from left to right and use a ruler to make straight lines.
Note that, for a mirror, R and f always have the same relationship to each other.
2. Express this relationship in equation form:
The drawing above should reflect (no pun intended) this relationship.
3. Repeat the same procedure for a convex mirror. Note that for a convex mirror parallel incoming
rays appear to come from F.
Concave Mirrors
1. Hold a concave mirror toward a distant object (such as a tree or building) and focus a distinct image
(of the tree or building) on a screen (piece of paper). Record the image distance and repeat for every
member of your group. Record the values of f:
2. favg =
a. How does this value compare with the value marked on the mirror?
b. Are the light rays from the object really hitting the mirror parallel? Explain.
c. Theoretically how far away would an object have to be for its light to actually be parallel?
In Geometric Optics ray diagrams are used to locate the image of an object and its size with only the use
of three rays – the parallel ray, the chief or radial ray and the focal ray.
3.
The parallel ray emerges from the object parallel to the principal axis. Where does it go after
reflecting off of a concave mirror?
4. The chief ray or radial ray passes through the center, C. Where does it go after reflecting off of a
concave mirror?
5.
Why does the radial ray reflect this way?
6. The focal ray passes through the focal point F. Where does it go after reflecting off of a concave
mirror?
The intersection of these rays identifies the position, size (and thus magnification), and type (upright or
inverted, real or virtual) of image.
7. In the space below, draw a spherical concave mirror labeling F and C. Draw an object (an upright
arrow will suffice) somewhere outside of F. Draw and label the three rays and locate the image.
Show the object and image distances, p and q, respectively.
8. Is the image upright or inverted?
9. Now hold a concave mirror at arm's length so that you can see your eye. At this distance your eye is
outside of F. Is the image you see consistent with your drawing above? Explain.
10. Draw a spherical concave mirror labeling F, and C. Draw an object somewhere inside of F. Draw and
label the three rays and find the image.
a. Where is the image located?
b. Could such an image be focused on a screen? Explain.
11. Where would an image be located if an object were placed at F?
12. Place the tip of a pencil at F of your concave mirror.
a. What do you observe?
b.
Comment on whether this procedure could be used to determine the focal length of a concave
mirror.
Convex Mirrors
1.
Draw a ray diagram for a convex spherical mirror. Label F and C. Draw an object to the left of the
mirror, draw and label the three rays – parallel ray, chief/radial ray and focal ray - then locate the
image.
2. Is your image upright or inverted?
3. Hold a convex mirror at arm's length and look at the image of your eye. Is the image you see
consistent with your drawing above? Explain.
4. Is the image real or virtual? How do you know?
5.
Can a convex mirror ever produce an inverted image? If your answer is yes, explain how.
The Mirror Equation
Materials: optics bench, incandescent light source, 50 mm concave mirror, viewing screen, crossed
arrow target, and three component holders.
Set up the light source at the far left end of the optics bench. Somewhere near the middle of the bench,
place the crossed arrow target (on a component holder). To the right of this, place the viewing screen
which should cover only half the hole in the component holder. This will allow light from the lamp's
filament to reach the mirror, which should be placed on the third component holder to the right of the
viewing screen as far as possible from the target (the object). Vary the position of the viewing screen
until the image of the target comes to the best focus.
1. Slowly increase the distance between the object and mirror.
a. As you increase the distance what do you have to do to the viewing screen to keep the best
focus?
b. What does the image look like when the object is as close to the light source as it can get?
c. Measure and record the image distance when the object is as close to the light source as it can
get.
q=
d. Is this about what you expected? Why?
2. Record the image distance (q) and image height (h') for the given object distances (p). Then calculate
the values in the last four columns using your values of p, q, h and h’.
p (mm)
q
h’
+
500
400
300
200
100
50
a. What is the relationship between the values in columns 4 and 5?
b. What is the relationship between the values in columns 6 and 7?
-
Express these two relationships as equations:
The Mirror Equation:
Magnification:
Questions
(1) What is the difference between a real and a virtual image?
(2) Suppose that you have two mirrors with equal radii of curvature except that one is a concave mirror
and the other is a convex mirror. Do they have exactly the same focal lengths? Explain.
(3) What is the significance of a negative magnification?
(4) Consider a plane mirror
a. What is the radius of curvature of a plane mirror?
b. Using the mirror equation, show (mathematically) that the image produced is always virtual.
c. Show (again, mathematically) that the image is always upright.
d. Are these last two results consistent with what you found in last week’s reflection and refraction
lab?