Lab 7 Conclusion
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Mechanical Engineering
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Feb 20, 2024
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Jessica Mouawad
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Lab 7 Conclusion: Combination of Lenses Conceptual: 1) This information is not su
ffi
cient because although a diverging lens will always produce a virtual image, when a converging lens is inside the focal point it also generates a virtual image. Therefore, you would also need the distance of the focal point from the object and the position of the lens in reference to that point. 2)
i)
ii) Data Analysis: 3)
i)
Yes you could accurately measure the focal length for 'lens 5' by using the setup from Steps B1-B3 because 'lens 5' is a single lens and therefore follows the thin lens equation. Thus, the focal length could be calculated using the object distance of the lens and object distance of the screen. The technique in steps B6-B11 of this experiment allowed the determination of the focal length of 'lens 5' by first using the average measured object distance (do
c
) and image distance (di
c
) to calculate the focal length of the combined lens 1 and lens 5 (f
c
) using the thin lens equation (1/f
c
= 1/do
c
+ di
c
). Then, f
c
was used to calculate the power of the combined lens 1 and lens 5 (P
c
= 1/f
c
), which was then used to calculate the power of lens 5 (P
5
= P
c - P
1
). Lastly, P
5
was used to determine the focal length of lens 5 (P
5
= 1/f
5
).
The uncertainties of the object distance and the image distance were determined by taking the absolute value di
ff
erence between of the inside (min) and outside (max) measurements of the width of lens and dividing by 2. The combined lens 1 and 5 focal length (f
c
) = 243mm +/- 5 mm, in which the uncertainty was determined by taking the absolute value di
ff
erence between the f
c(min)
and f
c(max)
and then dividing by 2.
ii) The focal length of lens 1 (f
1
)= 148mm +/- 10mm which was determined by:
1/f= 1/d
o
+ 1/d
i
f
1min
= 1/[(1/161)+ (1/941)]= 137mm
f
1max
= 1/[(1/188)+(1/968)]= 157 mm
f
1
= (137+157)/2 = 148 mm
uncertainty: |f
1min-
f
1max
|/2
|137-157|/2= 9.5 = +/- 10 mm
iii) The focal length of lens 5 (f
5
)= -370mm +/- 0.6
P
5
= P
c
- P
1
P
5
= 4.1 - 6.8 = -2.7
f
5
= 1/P
5
= -370mm uncertainty: |(P
c(min)
-P
1(min)
) - (P
c(max)
-P
1(max)
)|/2
|2.2 - 3.3|/2= 0.55 = +/- 0.6
4)
Yes, the focal length of lens 1 was determined to be 148mm and the value provided in the manual was around 150 mm therefore it is consistent. 5)
The image is real, magnified, and upright.
7
Screen
228.0 cm +/- 10.0 cm Lens 1
44.0 cm +/- 1.2 cm
Lens 2 104.1 cm +/- 1.4 cm
x= 0.0 cm
6)
combined focal length
d= 104.1 cm - 44.0 cm = 60.1 cm = 601 mm
1/f
c
= 1/d
o
+ 1/d
i
f
cmin
= 1/[(1/428)+ (1/1027)]= 302 mm
f
cmax
= 1/[(1/452)+(1/1055)]= 316 mm
f
c
= 309 mm +/- 7 mm
f
2(min)
= 1003 mm
f
2(max)
= 753 mm
uncertainty: |1003-753|/2 = +/- 125 mm
f
2
= 878 mm +/- 125 mm I
I
f
f
t
I
I
I
I
150
Fz
302
150
f
0.003
0.004
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