Dr. Bill Pezzaglia
CSUEB Physics
Physics 1780 Lab Winter 2015
Activity: Optics of Lenses & Mirrors
Page 1
2015Feb16
Lab Activity: Optics of Lenses & Mirrors
INTRODUCTION
Lenses and mirrors are, in general, large compared to the wavelength of light; therefore,
interference and diffraction effects can be neglected, and light can be treated as rays that travel in
a straight line. This approximation is called geometrical optics. In this approximation the
behavior of light at a boundary between two media is described by the law of reflection and
Snell’s law of refraction.
A lens is an image forming device, and the location of the image, for example, is determined by
Snell’s law. The characteristics of the image (real or virtual, upright or inverted, enlarged or
reduced) depend on the lens type, converging or diverging, and object location. The object
distance p, image distance q, and focal length f of a thin lens or a mirror are related by:
1  1  1
p
q
f
(1)
All distances are measured with respect to the lens. For a mirror the focal length f and the radius
of curvature R are related by:
f R
(2)
2
The magnification, M, produced by a lens is the ratio of the size of the observed image, h’, to the
objects actual size, h. The magnification is determined by the ratio of the image distance to the
object distance:
M  h'   q
h
p
(3)
The picture below, called a ray diagram, demonstrates how p, q, f, h, and h’ are all related. The
picture is created by first drawing a horizontal line from the top of the object to the lens. This
line is then continued straight through the focal point on the right hand side of the lens. The
second ray is drawn from the top of the object, straight through the middle of the lens, continuing
in the same direction on the other side. The image forms where these two lines intersect. In this
case the lens produces a real, inverted, image reduced in size.
h
h’
p
f
q
f
Figure 1: Lens Geometry
Dr. Bill Pezzaglia
CSUEB Physics
Physics 1780 Lab Winter 2015
Activity: Optics of Lenses & Mirrors
Page 2
2015Feb16
EXPERIMENTS
A. Measuring Focal Length: Distant Object Method
In this section you will use a simple method to estimate the focal lengths of lenses and mirrors.
The focal length of a converging lens may be estimated by forming the “real” image of a far
away object, where p >> f, then
1  1  1  1
f
p
q
q
(4)
Hence, the focal length f is approximately equal to the image distance q.
1. Converging Lens, measure focal length
While holding one of the converging lenses by its edges, project and image of a distance object
on a screen. Move the lens closer or further away from the screen until the image is in focus.
Measure the distance from the middle of the lens to the screen (q). Because this is a distant
object, the focal length is nearly equal to “q”. Make a sketch of your setup!
2. Other Measurements (for each make a sketch of setup, labeled with numbers):
 Repeat the measurement with the other converging lens
 Repeat the measurement with the converging mirror.
3. Data & Calculations
 Record data for all lenses/mirrors in tabular format. Give focal length in cm, and also in
Diopters (inverse meters).
Question 1. How do your measured values for the lenses compare to the true values of 5 cm
and 10 cm? Why would you expect to be slightly off? Do you think your estimate would
change if you went outside and used the sun as the object?
Question 2. Comment on the orientation of the images. Are they erect, inverted, reversed or
inverted and reversed?
B. Lens Combination Formula
Theory: Two “thin” lenses put together will behave as a single lens with focal length of:
1  1  1
(5)
fc
f1
f2
where f1 and f2 are the focal lengths of the individual lenses. Note, if you measure focal lengths
in “Diopters” (inverse meters), then the total focal length in Diopters, is simply the sum of the
two lenses (in Diopters).
1. Combined Lens: Use 5 and 10 cm lens, and measure the focal length of the combination.
Question 3: What is your measured focal length of the combination? Compare to the
expected value given by equation (5).
Dr. Bill Pezzaglia
CSUEB Physics
Physics 1780 Lab Winter 2015
Activity: Optics of Lenses & Mirrors
Page 3
2015Feb16
2. Measuring Focal Length of a Diverging Lens:
Diverging lenses (or mirrors): have a negative focal length and form “virtual” images on the
same side of the lens as the object. Hence we cannot use the “distant object” method to
determine the focal length because there the light does not converge to form a real image. To
measure the focal length of a diverging lens we combine it with a more powerful converging lens
f2, measure the focal length of the combination f, and then use equation (5) to get the focal length
of the diverging element f1.
Question 4: Report your measured focal length of the diverging lens. Be sure to show your
method, measurements, and calculations.
3. Eyeglasses
 Note a nearsighted person can see fine up close, but there is a maximum distance (called
the “far point”) past which things are fuzzy.
 For a nearsighted student, measure the focal length of their (diverging) glasses using the
same technique.
 Without wearing the glasses, have the student measure their “far point” (the maximum
distance they can see clearly).
Question 5: Compare the far point measurement with the (negative) focal length of the
glasses. Are they nearly the same?
C. Gauss’s Law of Optics
A lens is an image forming device, and the location of the
image, for example, is determined by Snell’s law. The
characteristics of the image (real or virtual, upright or
inverted, enlarged or reduced) depend on the lens type,
converging or diverging, and object location. The object
distance p, image distance q, and focal length f of a thin
lens or a mirror are related by:
1  1  1
(1)
p
q
f
In this section you will measure the image distance “q” for
various object distances “p” using your 10 cm lens. The
general set-up for the system is shown in the picture below.
Figure 2: Image Orientation
Lamp
Object
Lens
p
Screen
q
Figure 3: Setup for Experiment
Dr. Bill Pezzaglia
CSUEB Physics
Physics 1780 Lab Winter 2015
Activity: Optics of Lenses & Mirrors
Page 4
2015Feb16

Measure image distance (“q”) for various object distances (“p”).

Plot inverse image distance

Note if “q” is in meters, then 1/q is in Diopters

If the “thin lens law” is valid: then we have:

Hence we expect the plot to be a straight line with slope of 1, and the intercept give the focal
length of the lens in Diopters.
1
1
vs inverse object distance
.
q
p
Figure 4a: Sample Data Table
p (m) q (m) 1/p (D) 1/q (D) 0.1 0.233 10.00 4.29
0.15 0.131 6.67 7.62
0.2 0.108 5.00 9.29
0.25 0.097 4.00 10.29
0.3 0.091 3.33 10.95
0.35 0.088 2.86 11.43
0.4 0.085 2.50 11.79
0.45 0.083 2.22 12.06
0.5 0.081 2.00 12.29
0.55 0.080 1.82 12.47
0.6 0.079 1.67 12.62
0.65 0.078 1.54 12.75
1 1 1
  .
q f p
Figure 4b: Sample Graph
Question 6: Lens Law
(a) Is the lens law valid? (i.e. is the plot a line with slope of 1)
(b) What is the intercept in Diopters?
(c) What hence is the focal length of the lens?
D. Image Type and Size





This time, use the mirror to make a real image.
Set up a situation where “p” and “q” are different.
Measure the size of the object h and size of the image h (refer to lens example figure 1)
Compute the observed magnification: M=h’/h
Compute the expected magnification: M=-q/p
Question 7: Verify equation (3) is valid. In particular, interpret the meaning of the negative sign in
equation 3.
Dr. Bill Pezzaglia
CSUEB Physics
Physics 1780 Lab Winter 2015
Activity: Optics of Lenses & Mirrors
Page 5
2015Feb16
E. Virtual Images


Use a converging lens as a magnifying glass.
Draw what you see (somewhat subjective).
Question 8: When you look through the lens at an object,
is the image bigger or smaller than the object? Does the
image appear to be closer or further away than the object?
Is it erect, inverted, reversed or both? [Hint, make a
drawing of your setup].
Figure 5: Magnifying Glass
F. Telescope

Use long focal length lens Fo as
“objective”.

Use short focal length lens Fe as
“eyepiece”. The distance between the
lenses should be almost exactly the
sum of the two focal lengths.

Set up the telescope to view some
distant object.

Measure “apparent size” of object:
Using a ruler held at arms length,
measure the approximate size of the
object (naked eye). Call this so.

Measure “apparent size” of image: This is trickier. Use the same method to measure
the size of the image as seen through the telescope [this measurement requires you to
look at the ruler with your left eye while looking through the telescope with your right eye
and superimposing the images!]. Call this si.

Calculate observed magnification:

Calculate the expected (theoretical) magnification: M=Fo/Fe
M= si /so
Question 9: Telescope
(a) Summarize your setup
(b) Compare your observed magnification with the theoretical value.
(c) Is the image erect, reversed, inverted or both?
Dr. Bill Pezzaglia
CSUEB Physics
Physics 1780 Lab Winter 2015
Activity: Optics of Lenses & Mirrors
Page 6
2015Feb16
G. Microscope (if time, XTRA CREDIT)
A simple microscope has two lenses, an objective lens and an eyepiece lens. The image of the
objective lens is the object for the eyepiece lens and both lenses contribute to the magnification.
In this section you will build your own microscope with the +10 cm lens as the objective, and the
+5 cm lens as the eyepiece lens.
Object (
) Objective
Screen
Eyepiece
Lam
po  fo
pe  fe
qo
L
Figure 7: Microscope
1. The diagram above shows the general layout. Start by mounting all of these components on
the rail, turning on your lamp, and inserting the triangular screen grid as your object.
2. As you did above, form an image on the screen for p < q.
3. The eyepiece is used as a magnifier. Looking through the eyepiece, vary its position until you
see a sharp image of the rear of the screen. Remove the screen. Viewing the image will be
more comfortable if you turn off the lamp behind the wire mesh and shine light from a
gooseneck lamp on the mesh. Viewing the mesh in this way, vary the position of the lenses to
obtain the sharpest possible image.
4. Objective Magnification: The lateral magnification of the objective lens, Mo, is:
q
Mo   o
(6)
po
We approximate this lateral magnification in the following way. Since qo > po we will
approximate p0 ≈ fo. Also the focal length fe is small compared to qo, thus qo ≈ L. Therefore the
magnitude of the objective magnification is:
Mo  L
(7)
fo
Question 10. What is the calculated magnification of your objective lens using the
approximation above?
Question 11. The eyepiece is used as a simple magnifier, and the angular magnification of the
eyepiece is Me = 25(cm)/fe, where fe is the focal length of the eyepiece lens. What is the
magnification of your eyepiece?
Question 12. Calculate the overall magnification Mo  Me of your microscope.
You can change the magnification at will, just by changing L. Move the shorter fe lens away from
the lamp, and adjust the other fo lens; the image should be larger but of lower quality.