Pinhole Camera Investigation
description
Transcript of Pinhole Camera Investigation
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Pinhole Camera Investigation
By Oscar G.M and David Mayer
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IntroductionPurposes: • To investigate the relationship between object distance and image
height while maintaining a constant image distance, and a constant object height.
• To investigate the relationship between object height and image height while maintaining a a constant object distance, and a constant image distance.
• To investigate the relationship between image distance and image height while maintaining a constant object height, and a constant object distance.
• To observe the effects of increasing the diameter of the pinhole, and creating more than one pinhole.
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Hypotheses
• If we decrease the object distance, then the image height will increase.
• If we increase the object height, then the image height will increase as well.
• If we increase the image distance then the object distance will increase as well.
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Equipment
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Setup
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Part 1: Image Height vs. Object Distance
Image Distance: 0.16 m Object Height: 0.023m
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Mathematical AnalysisImage Height vs. Object Distance
1. Image Height Hi Object Distance do
2. Hi α 1/ do
3. Hi = k* 1/ do
4. k = ∆ Hi / ∆ 1/ do
5. k = 0.00399 m/1/m6. Hi = 0.00399 m/1/m * 1/ do
Let’s look at those units… m/(1/m) m*(m/1) m2
Hmm, m2 … what were our constants again? Image distance: 0.16 m, object Height: 0.023m. m*m m2 .
0.023m * 0.16 m = 0.00368 m2 .
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Meaning?
0.023m * 0.16 m = image distance * object height Image distance = di
And
Object height = HoSo
Slope= Ho* di
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Error CalculationsAccepted Value=0.16m*0.023m=0.00368m2 Experimental Value=0.00400m2
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Part 2: Image Height vs. Object Height
Object Distance: 0.20 m Image Distance: 0.16 m
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Mathematical AnalysisImage Height vs. Object Height
1. Image Height Hi Object Height Ho
2. Hi α Ho
3. Hi = k* Ho
4. k = ∆ Hi / ∆ Ho
5. k = 0.812 mm/mm6. Hi = 0.812 mm/mm * Ho
Let’s look at those units once more… mm/mm 1This looks like a ratio…our constants were object distance: 0.20 m, image
distance: 0.16 mConstant / Constant = 0.812
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Meaning?
The only way for this to occur is if we divide the smaller number by the larger number to give us something
less than 1. 0.16 m / 0.200 m = 0.800
Slope= di/do
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Error Calculations Accepted Value=0.16m/0.2m=0.800 Experimental Value=0.812
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Part 3: Image Height vs. Image Distance
Object Height: 0.023 m Object Distance: 0.200 m
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Mathematical AnalysisImage Height vs. Image Distance
1. Image Height Hi Image Distance di
2. Hi = α di
3. Hi = k*di
4. k = ∆ Hi / ∆ di
5. k = 0.100 m/m6. Hi = 0.100 m/m *di
Looks like a ratio once more…our constants were object height: 0.023 m, object distance: 0.200 m
Constant / Constant = 0.100
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Meaning (last cheesy time)?
0.023m / 0.200 m = object height / object distanceSo
Slope= Ho/ do
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Error CalculationsAccepted Value=0.0230m/0.200m=0.115 Experimental Value=0.100
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Pinhole
Light Source with rays
ObjectHo
do
Hi
di
The Basic Principle
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Ho
Hi
di
Original
do
Part 1: Changing Object Distance
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Ho
do
Hi
di
Original
Part 2: Changing Object Height
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Ho
do diHi
OriginalPart 3: Changing Image Distance
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2 More Ways to See This RelationshipJoint Variation:
Hi α 1/ do
Hi α Ho
Hi α di
Hi α Ho * di /do
Hi = Ho * di /doThere was no constant of proportionality
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Geometry
doHi
di
Ho
θ
θ
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More Pinholes
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Bigger Diameter Pinhole
Bigger Hole = Brighter, Blurrier Image
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The End