Download Geometrical Optics and Lenses

Geometrical Optics and Lenses
R.L.Griffith,M.R.Levi,D.Cartano
ABSTRACT
A test concerning the principles governing lenses and mirrors was conducted to verify the
accuracy of the theory. A spherometer was used to measure the radius of curviture for all
lenses and mirrors. Two converging lens, a diverging lens and a mirror were used during
this experiment. The converging lens consisted of a long focal length and a short focal length
with n = 1.53 for both of them. Measurements of the location of the lens and the location of
both object and image were recorded and are given in the tabular summary. The converging
lens were both used independently for calculations. The short focal length converging lens was
than used in combination with the diverging lens and measurements were also recorded for
both image and object, to calculate the focal length of the diverging lens. The last test was
conducted using the mirror and the image location and object location were also recorded. All
eight ray diagrams are included at the end of this report. The experimental errors were within
18% and we concluded that the theory concerning lenses and mirrors can be used to model the
behavior of lenses and mirrors
Subject headings: Optics, Lenses
1.
Introduction
where R is the radius of curvature for the mirror.
R is calculated for both mirror and lenses using
A lens is merely a carefully ground or molded
piece of transparent material which refracts light
rays in such as way as to form an image. Lenses
can be thought of as a series of tiny refracting lenses, each of which refracts light to produce their own image. When these prisms act
together, they produce a bright enough image
focused at a point. Lenses are commonly used
to form images by refraction in optical instruments such as telescopes, microscopes, and cameras. Images created with concave mirrors are
always real and inverted. Many optical instruments also use mirrors to focus light to a point.
We will be calculating the focal lengths for all
the lenses and mirrors, both experimentally and
theoretical. The experimental focal lengths can
be calculated using the lens equation
1
1 1
= +
f
p q
s
l2
+
(3)
2 6s
where s is the sagitta of the lens. The sagitta of
the lens was measured using a spherometer. The
l is the distance between the legs of the spherometer. The theoretical values for the focal lengths
were calculated using the lens makers’ equation
1
1
1
= (n − 1)
−
(4)
f
R1
R2
r=
Where R1 and R2 are the radius of curvature
of the lenses calculated using equation 3. The
errors for this lab will be calculated using
ftheory − fexp × 100 = %
(5)
ftheory
2.
(1)
2.1.
where f represents the focal length of the lens,
p represents the object location and q represents
the image location. We will be using equation 1
to calculate all the experimental values for the
focal length. The focal length for the mirror can
be calculated using
f=
R
2
Method
Equipment Used
Equipment
Two convex (positive) lens
One concave (negative) lens
One concave mirror
one light source
One screen
Vernier caliper
One optical bench
(2)
1
Model
n/a
n/a
n/a
n/a
n/a
n/a
n/a
2.2.
Lens
Long Converging
Long converging
Short converging
Short converging
Mirror
Mirror
converging diverging
converging diverging
Results
Procedure
The procedures for this lab are outlined in
the Physics 103 lab manual. The optics bench
apparatus is set up according to the diagram in
the lab manual. The first trial is conducted with
the long focal length converging lens. The second
trial is performed using the short focal length
converging lens. Two trial are performed on each
lens, one when p > q and one with p < q. this
will be performed for each lens and set of lenses,
including the concave mirror.
3.
4.
p<q
p>q
p<q
p>q
p<q
p>q
p>q
p<q
fexp cm
19.74
19.11
10.18
9.25
23.21
23.57
-8.13
-9.70
Conclusion
This lab was conducted to get a better understanding on the nature of light and how lens are
used to create images. We concluded that the
theory concerning lenses and mirrors hold under
scrutiny. The results we acquired were accurate
to within 18 %, except for the test involving the
concave mirror where we acquired a 50 % error.
The errors for this lab could have been acquired
by a few different parameters. A source of error
can be credited to the precision of our measurements when recording object location, lens location, and image locations. The image location
was the hardest parameter to record, due to the
fact that there is a window of ±5cm for which
the image appears to be in focus. The mirror
trial can be affected by this factor the most and
therefore a 50 % error can be accounted for by
that. This lab has concluded that the equations
derived in the introduction section are valid approximations for testing lenses and mirrors.
Results and Discussion
There are four different trials in the lab. The
first two include using the positive converging
lens, the long and short focal length. The lenses
are used to focus a light source onto a white
screen and the location of the lens, object, and
image are recorded. the third trial is conducted
using the short positive lens and a diverging lens,
and the fourth trial is conducted using the concave mirror. To find the experimental value of
the focal length for the converging to diverging
lens combination we must first find the position
for object 2 and then the position for image 2 and
find the focal length using equation 1. Recording the image location and object location we can
then use equations 1 and 2 to calculate the experimental values for the focal lengths and compare them to the theoretical values calculated
with equation 3. we can then make error measurements to see if the experiment agrees with
theory .
5.
Acknowledgements
The author would like to thank Roni and
David for their help with this experiment.
REFERENCES
Los Angeles City College Lab Manual Physics
103.
3.1.
Data and Calculations
Lens
Long Converging
Long converging
Short converging
Short converging
Mirror
Mirror
converging diverging
converging diverging
Measured quantities
p<q
p>q
p<q
p>q
p<q
p>q
p>q
p<q
p (cm)
32.2
41.7
10.7
67.2
28.5
61.0
67.2
21.8
q (cm)
47
37.5
68.5
12
131.3
39.1
12.1
50.6
2
This 2-column preprint was prepared with the AAS
LATEX macros v5.2.
ftheory cm
16.41
16.41
9.4
9.4
52.1
52.1
-9.81
-9.81
Error(%)
20.2
16.4
8.2
1.5
54.7
54.7
17.1
1.12