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(JL)^2 [aka Jackie and Jocelyn]. Converging mirrors. Purpose. Determine the relationship between object distance and image distance for real images in a concave spherical mirror Determine the relationship between object height and image height for a set object distance. Hypotheses. - PowerPoint PPT Presentation
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Converging mirrors(JL)^2 [aka Jackie and Jocelyn]
Purpose
Determine the relationship between object distance and image distance for real images in a concave spherical mirror
Determine the relationship between object height and image height for a set object distance
Hypotheses
The inverse of image distance will be linearly related to the inverse of object distance
The object height will be directly proportional to image height
Focal Length
Focal point – where rays parallel to the principal axis come to a focus
Focal length – distance between focal point and center of the mirror
Determining Focal Length Set curved mirror on track facing an
open window. Set screen on track between window
and mirror. Adjust distance between screen and
mirror until focused image (far away object through window, like a power pole) appears on the screen. Measure this distance with meter stick.
Experiment Diagram
Procedure – Part 1 Place object 15 focal lengths from mirror using cart tracks. Place the screen between mirror and object/light source
(see diagram). Move the screen until a focused image of the object
appears on the screen. Measure and record the image height that appears on the
screen and the distance between the screen and the mirror (image distance).
Decrease object distance by 1 focal length and repeat process until 3 focal lengths away from mirror.
Change distance increments to 5 cm. Continue process until 2 focal lengths away.
Reduce distance increments to 1 cm. Continue process until 1 cm less than 1 focal length away.
Part 1 Data
Sample Calcs
1/object distance = (1/do)
Example:1/do = 1/390 cm 1/do = 0.003 1/cm
1/image distance = (1/di)
Example:1/di = 25 cm 1/di = 0.040 1/cm
Mathematical Analysis
1/di 1/Image distance1/do 1/object distance
y = mx + b1/di = k (1/do) + bk = Δ(1/di)/Δ(1/do)
k = -1.05 1/cm / 1/cmk = -1.05
b = 0.0419 1/cm1/di = -1.05 (1/do) + 0.0419 1/cm
All slopes and values by LoggerPro
Error analysis: k
Accepted Value: 1Experimental Value (Source: magnitude of 1/di vs. 1/do graph slope): 1.05 ABS error: ǀAccepted value-Experimental valueǀ
ǀ 1 – 1.05 ǀ 0.05
Relative error: ABS/accepted value(0.05)/ (1)0.05 5% error
Error analysis: b
Accepted Value: 1/focal length = 1/26 cm = 0.0385 1/cmExperimental Value (Source: y-intercept of 1/di vs. 1/do graph): 0.0419 1/cm ABS error: ǀAccepted value-Experimental valueǀ ǀ 0.0385 1/cm – 0.0419 1/cm ǀ 0.0034 1/cmRelative error: ABS/accepted value(0.0034 1/cm)/ (0.0385 1/cm)0.0883 8.8% error
Error discussion
The method for taking data for this part largely relied on eyeballing distances and heights, so that was probably the largest source of error.
Also, for distance, we used a ruler to measure distances, which we had to constantly reset—so distances may not have been consistent, esp. with room darkness.
Results
1/di = b - k(1/do)k = 1
b = 1/f1/di = 1/f - (1/do)1/di + 1/do = 1/f
Part 2/3 procedure Place mirror on stand, at head of track. Use large lamp as light source. Place smallest arrow
card in front holder. Move light source 1.5 focal lengths from mirror.
Place screen between light source and mirror. Do not block light source. Adjust mirror so that image appears on screen.
Move screen until image focuses. Measure image height and object height with ruler. Repeat process for all arrow cards, recording the
height of actual arrow as well. Move light source until it is 2.5 focal lengths from the
mirror and repeat entire process.
DIAGRAM
Data
Math analyses part 2
hi Image heightho Object height
hi ∝ ho y = mx
hi = k (ho)k = Δhi / Δho
k = 1.89 cm/cmk = 1.89
hi = 1.89 ho All slopes and values by LoggerPro
Error part 2
Accepted Value: f/(do – f) = 26 cm / [1.5 (26cm) – 26 cm] = 2Experimental Value (Source: magnitude of hi vs. ho graph slope): 1.89 ABS error: ǀAccepted value-Experimental valueǀ ǀ 2 – 1.89 ǀ 0.11Relative error: ABS/accepted value0.11/20.055 5.5% error
Error discussion
Same as in part 1: eyeballing distances was the largest source of error, as well as estimating where the image focused exactly.
Results part 2
hi = k(ho)
k = f/(do – f)
hi = [f/(do – f)](ho)
Part 3 data
Graph part 3
Math analysis part 3
hi Image heightho Object height
hi ∝ ho y = mx
hi = k (ho)k = Δhi / Δho
k = 0.593 cm/cmk = 0.593
hi = 0.593 ho All slopes and values by LoggerPro
Error part 3
Accepted Value: f/(do – f) = 26 cm / [2.5 (26cm) – 26 cm] = 0.667Experimental Value (Source: magnitude of hi vs. ho graph slope): 0.593 ABS error: ǀAccepted value-Experimental valueǀ ǀ 0.667 – 0.593 ǀ 0.074Relative error: ABS/accepted value0.074/0.6670.111 11% error
Error discussion
Same as in parts 1 and 2: eyeballing distances was the largest source of error, as well as estimating where the image focused exactly.
Results part 3
[This might possibly look familiar.]
hi = k(ho)
k = f/(do – f)
hi = [f/(do – f)](ho)
Let’s put it all together!From experiments 2 and 3:hi = [f/(do – f)](ho)hi / ho= f/(do – f)
From experiment 1: 1/di + 1/do = 1/f
So:1/di = 1/f- 1/do1/di = do/fdo- f/fdo1/di = (do- f)/fdodo/di = (do- f)/fdi/do = f/(do- f)
hi / ho= di/do
Ray diagram: Object outside C
Ray diagram: at C
Ray diagram: between C and F
Ray diagram: inside F
Graphical representation:
THE END