Physics3LC Wk4 Lenses
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University of California, Irvine *
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Course
47180
Subject
Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by AmbassadorFreedomAnt102
Week 4 Lab Report – Lenses
Date: 10/26/23
Section: T
hursday 2:30
Lab Instructor: Alex
Lab Partners: 1.
Kalysa Bui (85561106)
2.
Miles Nguyen (47028628)
Total Score: /24
4.3.2 Focal length of a lens
(6 points)
Goal: Measuring the focal length of your lenses and verify Eq. 4.2
Draw a ray diagram (1 point)
Image 4.3.2 - 1
Overall setup for experiment 4.3.2.
Image 4.3.2 - 2
Ray diagram of a convex lens, with focal
length (f), object distance (o), and image
distance (i).
1
Data and Analysis (2 points)
o (m)
o (cm)
i (cm)
f (cm)
using lens formula
f (cm)
assuming
f=i
*Discrepan
cy:
lens formula vs.
12 cm (%)
*Discrepan
cy:
f=i vs. lens formula (%)
0.798
79.8
13.4
11.5
13.4
4.26
15.3
*For the discrepancies, be sure to use the correct theoretical values
Show all your calculations here (2 points).
Thin lens equation (1 point)
f (cm) using thin lens formula: 1/o + 1/i = 1/f
f = 1
1
o
+
1
i
f = 1
1
79.8
+
1
13.4
f = 11.5
Discrepancy lens formula vs. 12cm: %
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
11.5
−
12
|
|
11.5
+
12
2
|
×
100%
% discrepancy = 4.26%
Discrepancy f=i vs. lens formula
%
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
11.5
❑
−
13.4
|
|
11.5
+
13.4
2
|
×
100%
2
% discrepancy = 15.3%
3
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4.3.3 Thin Lens Equation
(thicker profile lens) (7 points)
Schematic diagram of experimental setup:
Image 4.3.3 - 1
Overall setup.
Data and Analysis
(3 points)
Trial #
o (cm)
i (cm)
f (cm)
from o and i using lens formula
Vertica
l size of
lit object (cm)
Vertical
size of image on the screen (cm)
M (measured)
vertical
M
(theory
)
M=-i/o
Discre-
pancy
for focal length, f (%)
Discre-
pancy for M (%)
1
22.2
6.3
4.91
3.3
1.1
-0.33
-0.284
1.82%
15.0%
2
12.4
9.6
5.41
3.3
2.8
-0.848
-0.774
7.88%
9.12%
Show calculations leading to the entries for both trials in the above tables. For M we consider only the vertical magnification.
Is the object inverted? (1 point)
The object is inverted.
Show calculations for M based on the vertical sizes of the object and the image (1 point)
Show calculations for M based on the thin lens equation (1 point)
Trial 1
4
f from o to i
1/o + 1/i = 1/f
f = 1
1
o
+
1
i
f = 1
1
22.2
+
1
6.3
f = 4.91
M Measured -
height of the object : 3.3 cm
-
height of the image: 1.1 cm (inverted)
-
size of image / size of object = -0.33
M Theory M = -i/o M = -6.3/22.2
M = -0.284
Discrepancy f: %
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
4.91
−
5
|
|
4.91
+
5
2
|
×
100%
% discrepancy = 1.82%
Discrepancy M:
%
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
.284
−
.33
|
|
.284
+
.33
2
|
×
100%
% discrepancy = 15.0%
Trial 2
f from o to i
5
1/o + 1/i = 1/f
f = 1
1
o
+
1
i
f = 1
1
12.4
+
1
9.6
f =5.41
M Measured -
height of the object : 3.3 cm
-
height of the image: 2.8 cm (inverted)
-
size of image / size of object = -0.848
M Theory M = -i/o
M = -9.6/12.4
M = -0.774
Discrepancy f: %
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
5.41
−
5
|
|
5.41
+
5
2
|
×
100%
% discrepancy = 7.88%
Discrepancy M:
%
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
0.848
−
0.774
|
|
0.848
+
0.774
2
|
×
100%
% discrepancy = 9.12%
Draw a ray diagram for one of your conditions of o and I
(1 point)
6
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Image 4.3.3 - 2
Ray diagram of conditions o = 12.4 cm and i=
9.6 cm.
7
4.3.4 Magnifying Glass
(6 points)
Goal: Construct a simple magnifier
Image 4.3.4 - 1
Overall setup.
Data and Analysis Object
o (cm)
Image Inverted?
(yes or no)
i (cm)
(theo-
retical)
Sign of i (+ or −
)
Screen
Observation
Lit Object
10.0
no
-76.7
-
no image Show the calculations leading to the entries in the above table. (2 points)
1/o + 1/i = 1/f
i = 1
1
f
−
1
o
i = 1
1
11.5
−
1
10
i = -76.7
Is the image real or virtual? (1 point)
The image is real.
Although you can see an image of the lit object, there is no projected image on the screen. Why? (1 point)
8
The lens is within the focal length meaning that refracted rays neither converge nor diverge and the distance from the object to the image will be infinite as the rays travel parallel and never converge to form an image or diverge to create a virtual image.
Draw a ray tracing diagram showing o, f, and i. Be sure to label all the distances in the diagram. (2 point)
4.3.5 Microscope
(5 points)
Goal: Construct a simple microscope
4.3.5 - Overall setup
Set your lamp behind the ruled screen; the ruled screen is now your object. Make sure your lamp is at a low brightness to make the rest of this lab easier.
(You do not
need to place a sheet of paper between the lamp and the ruled plastic square, at least
not at first; you may in the final step, however.)
Draw a schematic diagram of the experimental setup.
9
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Table for 1
st
lens only (2 points)
o
1
(cm)
i
1
(cm)
Horizontal size of transparent ruled screen
(cm)
Horizontal size of image [on the white screen] (cm)
M
(theoretical)
for 1
st
lens
M
(measured)
For 1
st
lens
Discrepancy
M (%)
For 1
st
lens
17.0
55.5
5
12
-3.26
-2.4
30.4%
Table with the second lens included - full microscope (3 points)
location of
second lens
on optical
bench (cm)
L (cm):
distance
between
your eye
and the
object (the
ruled
screen)
f
2
(cm)
(should be
the one
calculated
in 4.3.3)
number of
magnified
divisions which match
the full width
(80 mm) of
the ruled
screen, see
explanation
below
m:
experimenta
l
m:
theoretica
l
%
discrepan
--cy of m
61
67
4.91
4
20
44.5
76.0%
Show your calculations of the experimental and theoretical magnification values for M and m, and their discrepancies in the table. experimental m = width of ruled screen/magnified divisions
m= 80/4
m=20
10
m theoretical:
= 1
/01 2 𝑚 𝐼 𝐿
𝑓
m = (55.5)(67)/(17.0)(4.91)
m = 44.5
%
discrepancy
=
|
X
1
−
X
2
|
|
X
1
+
X
2
2
|
×
100%
%
discrepancy
=
|
44.5
−
20
|
|
44.5
+
20
2
|
×
100%
% discrepancy = 76.0%
Additional explanation to the procedure to determine magnification of the microscope:
Manual:
“The next procedure takes some care. While viewing the magnified image through one eye, simultaneously view the ruled screen directly (i.e., without magnification) with your other eye. You may find moving your head a little distance sideways helps coordinate your eyes. Record the
number of magnified divisions which match the full width (80 mm) of the ruled screen. The ratio of 80 mm to the number of magnified divisions filling the screen is thus your experimental value for the microscope's magnification.”
Though this is explained accurately, it may be tricky to know what this actually means without a visual. Thus, we have provided a sample image/calculation. (In this particular case, the ruled screen was set up upside-down, while the image is upright, so the magnification, m, is negative
.)
11
In this image, the observer is looking through the second lens, and has focused their ‘eyes’ (note:
this is an image taken from a camera, but you would do it with your eyes in the lab) so that they can see the 80 mm plate, as well as its magnified image. In this case, we are looking to see how many magnified divisions the ruled screen fits into, which is, roughly, 2.5 magnified divisions. The ruled screen is 80 mm wide, so, to find the experimental value for the microscope’s magnification, m, we take -80/2.5 = -32. Your number of magnified divisions will probably be different, but otherwise you will do something very similar.
12
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