mxm

7/18/2019 mxm

http://slidepdf.com/reader/full/mxm 1/18

23/02/14 Django Trueman-Greinke

Quality of measurement report.Django Trueman-Greinke-Group B

Determining the focal length of a lens.

Contents:

Aim: Page 2

Background physics:

Page 2

Preliminary Method:

Page 2

Method: Page 3

Risk Assessment:

Page

Results: Page !

"raphs: Page #

Anomalies and $rrors:

Page %

Analysis: Page %

&ross checking of results:

Page '

&onclusion: Page ()

*mpro+ements:

Page ((

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Aim:

To fnd out the most ee!ti"e #a$ o% determining the %o!a& &ength o% a &ens'

Background Physics:

( ke$ pie!e o% )a!kground ph$si!s to make m$ e*periment ee!ti"e is that the

%o!a& &ength is dire!t&$ re&ated to the distan!e %rom the &ens to the o)je!t and the

distan!e %rom the &ens to the image' The %ormu&a %or is +(,+-(,u(,f , this !an )e

rearranged to +(,f-(,+/(,u,' n this e.uation +f , is the %o!a& &ength ++, is the

image distan!e and +u, is the o)je!t distan!e u is a&#a$s negati"e'

The "aria)&es %or the e*periment are as %o&&o#s'

ndependent Distan!e %rom the &ens to the o)je!t u'Dependent Distan!e %rom the &ens to the image +'

ontro& The si5e and po#er o% the &ens'

The shape o% the &ens'

The position o% the )u&)'

% the theor$ is !orre!t then ea!h o% the "a&ues %or u and + shou&d gi"e the same

"a&ue %or f using the e.uation a)o"e'

n m$ graph shou&d get a straight &ine #ith the e.uation +y-m0c, 6here +y, is

1/mage distan!e +m, is 1 the !&oser it is to 1 the more a!!urate m$

e*periment +0, is 1/7)je!t distan!e and +c, is 1/%o!a& &ength' 8sing this graph #i&& easi&$ )e a)&e to #ork out the %o!a& &ength )$ di"iding 1 )$ c'

Preliminary Method:

set up the e.uipment as sho#n in the diagram Page 3' then %ound the

appro*imate %o!a& &ength o% the &ens and pi!ked one #ith a medium %o!a& &ength'

This a&&o#ed me to measure a &arge num)er o% dierent distan!es #ith a good

amount o% inter"a&s )et#een ea!h "a&ue' then took se"era& measurements and

%ound out that a suita)&e inter"a& to measure ea!h "a&ue #as a 9!m dieren!e'

then %ound that the &ens #as suita)&e %or measurements )et#een 20!m and

:0!m'

This in%ormation sho#s me that m$ e*periment shou&d )e set up so the &ens is

20!m a#a$ %rom the o)je!t and then mo"ed a#a$ at 9!m inter"a&s unti& a

suita)&e num)er o% data points are !o&&e!ted' ;or e*amp&e up to <9!m a#a$ %rom

the o)je!t'

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Method:

$1uipment:

=eter ru&er To measure the distance between the bulb and the

lens, and the lens and the screen. This should be used

as it long enough to take all measurement from

without needing to take multiple measurements, like

you would with a 30cm ruler.

6hite s!reen As a screen to view the image on, white is good as it

creates good contrast allowing it to be easy to tell

when the image comes into focus.

;i*ed )&o!ks To place the lens and the bulb on securely, so they

don’t move and aect the results.

(djusta)&e )&o!k To place the screen on so it easily adusted without

having to og the entire apparatus.

G&ass on"e* >ens To proect the image of the !lament onto the screen.

"lass should be used as it is easy to clean and plastic

can become very dirty easily.

?a$ )o* #ith f&ament )u&) To create the image of the !lament which would

be proected onto the screen by the lens.

Diagram:

3 | P a g e

1/Distan!e %rom the &ens to the

1 / D i s t a n ! e % r o m t h

e

& e n s t o t h e i m a g e

m - 1 2

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etting up the e1uipment.

@et up the e.uipment as sho#n in the diagram'

he e0periment.

1' Position the &ens 20!m a#a$ %rom the )u&) and mo"e the s!reen so that

the image !omes into %o!us' ?e!ord the distan!e %rom the image to the

&ens in the ta)&e'2' =o"e the &ens )a!k 9!m and mo"e the s!reen so that the image is in %o!us

again' ?e!ord the distan!e %rom the image to the &ens in the ta)&e'3' ?epeat step 2 unti& there are 10 dierent resu&ts'4' ?epeat step 1 2 and 3 unti& there are 9 dierent resu&ts %or e"er$

measurement'9' ;ind the a"erage "a&ue %or ea!h &ength'<' Ae*t #ork out the %o!a& &ength %or ea!h dierent resu&t' To #ork out the

%o!a& &ength the e.uation is 1/"1/uC1/% or 1/"-1/u1/%'

u is the o)je!t distan!e the distan!e %rom the &ens to the o)je!t this isa&#a$s negati"e

" is the image distan!e the distan!e o% the s!reen %rom the &ens #hen the

image is in %o!us

% is the %o!a& &ength this is #hat #e,re tr$ing to fnd'

$rrors.

There !ou&d )e a random error as to #hen the image is in %o!us as it is hard to

te&& #hen an image is in e*a!t %o!us'

There !ou&d )e a sma&& s$stemati! error in the distan!e %rom the &ens as the ru&er

on&$ measures in mm so there !ou&d )e up to a 0'9mm error'

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Risk Assessment:

Risk o 4ho A+oidance

>ens or )u&) g&ass

)reaking

#$uipment

%e

&e careful when carrying

around and make sure

securely in place when

set up.

;au&t$ #iring in )u&) or

po#er )o*'

#$uipment

%e

"et teacher to check

wiring.

>ight )u&) )urning hand' %e

'thers

(o not touch bulb when

on and wait for it to cooldown after use. Trip ha5ard %rom )ags' %e

'thers

%ake sure ha)ards are

safely put out of the way.

Results:

Distance from the lens to theo56ect 7m8 9).))2

Distance from the lens to the image7m8 9 ).))!

est ( est 2 est 3 est est !

-0'200 0'<: 0'<<< 0'<4E 0'<94 0'<<:

-0'290 0'40< 0'40: 0'9:: 0'3E 0'401-0'300 0'311 0'31: 0'302 0'30E 0'309

-0'390 0'2<4 0'23 0'2<4 0'21 0'2<<

-0'400 0'24E 0'24E 0'292 0'244 0'24

-0'490 0'231 0'22< 0'22E 0'230 0'231

-0'900 0'220 0'21E 0'21 0'219 0'21:

-0'990 0'210 0'211 0'20E 0'20: 0'20E

-0'<00 0'20E 0'202 0'202 0'201 0'211

-0'<90 0'1E< 0'1E: 0'1E9 0'1E< 0'1E3

Date

10/02/20

14

10/02/20

14

11/02/20

14

11/02/20

14

11/02/20

14

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This !&ear&$ sho#s that test 3 %or the -0'290 distan!e %rom the &ens to the o)je!t

#as anoma&ous and shou&d there%ore not )e used %or in an$ !a&!u&ations' The rest

o% the data is !on!ordent #ith ea!h other and is there%ore "a&id to use'

$rror Analysis

Distance from thelens to the o56ect

7m8 9).))2

Distance from the lens to theimage 7m8 9 ).))!

est(

est2

est3

est

est!

A+erage

Range

pread

-0'200 0'<: 0'<<< 0'<4E 0'<94 0'<<:0'<<3

0'02E

0'0149

2'2

-0'290 0'40< 0'40: 0'9:: 0'3E 0'4010'403

0'011

0'0099

1'4

-0'300 0'311 0'31: 0'302 0'30E 0'3090'30E

0'01< 0'00:

2'<

-0'390 0'2<4 0'23 0'2<4 0'21 0'2<<0'2<:

0'00E

0'0049

1'

-0'400 0'24E 0'24E 0'292 0'244 0'240'24:

0'00: 0'004

1'<

-0'490 0'231 0'22< 0'22E 0'230 0'2310'22E

0'009

0'0029

1'1

-0'900 0'220 0'21E 0'21 0'219 0'21:0'21:

0'00

9

0'002

9

1'

1-0'990 0'210 0'211 0'20E 0'20: 0'20E 0'20E 0'00 0'001 0'

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3 9

-0'<00 0'20E 0'202 0'202 0'201 0'2110'209 0'01 0'009

2'4

-0'<90 0'1E< 0'1E: 0'1E9 0'1E< 0'1E30'1E<

0'009

0'0029

1'3

;ormu&a %or per!entage error Fma*-min/a"erage * 100

Graphs:

| P a g e

1/Distan!e %rom the&ens to the o)je!t m-

1 0'002

1/Distan!e %rom the&ens to the image

m-1 0'009

-9'000 1'9:0

-4'000 2'4:1

-3'333 3'23<

-2':9 3'31

-2'900 4'032

-2'222 4'3<

-2'000 4'9:

-1':1: 4':9

-1'<< 4'::

-1'93: 9'102

;ocal length of a lens: *nitial

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7n graph $ p&ots are 1/image distan!e

* p&ots are 1/o)je!t distan!e

$ inter!ept is 1/positi"e %o!a& &ength

* inter!ept is 1/negati"e %o!a& &ength

Anomalies and Errors:

$1uipment suita5ility and cali5ration: =$ e.uipment used #as %air&$

a!!urate as there #as no major s$stemati! error' The on&$ noti!ea)&e s$stemati!

#as due to the imper%e!t !ur"ature o% the &ens' To !a&i)rate m$ e.uipment had

to re!ord #here the o)je!t #as on the ru&er as there #as no #a$ to make it

e*a!t&$ 5ero' To a!!ount %or this simp&$ remo"ed the "a&ue o% #here the o)je!t

: | P a g e

$1'01<<*C<'<1<2

H nter!ept <'<1<2 0'2E 4'3:I

m-1

J nter!ept -<'90:2 0'19 2'30Im-1

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#as %rom the "a&ue %or #here the distan!e #here the &ens #as this made sure

there #asn,t a s$stemati! error %rom the ru&er'

Anomalies: had one anoma&ous resu&t' t #as the third test #hen the distan!e

%rom the &ens to the o)je!t #as -0'29 m'

$rrors: =$ data is !&ear&$ repeata)&e as the ma*imum per!entage error is on&$2'<I' This means that a&though not per%e!t m$ data #as &arge&$ !onsistent and

is repeata)&e' =$ gradient is not one this is #hat it shou&d )e ho#e"er it is on&$

0'02 o' t is o )e!ause the image o% the f&ament is not !&ear and there%ore

diK!u&t to te&& #hen it e*a!t&$ in %o!us' (&so it !ou&d )e o due to the %a!t that

the &ens might not )e per%e!t&$ !ur"ed' The !ur"ature to the &ens is a s$stemati!

error as is the !&arit$ o% #hen the image is in %o!us' The !&arit$ o% the image #as

m$ )iggest error'

Analysis:

=$ graph sho#s that the $ inter!ept is <'<1<2 and the * inter!ept o% -<'09:2' This gi"es an a"erage %o!a& &ength o% <'9<22 #ith a per!entage error o% 3'39I'

This is 1/;o!a& &ength so the %o!a& &ength is 1/<'9<22 or 0'19 #ith the same

per!entage error'

;ocal <ength of lens: ).(!m 3.3!

Cross Checking of results:

nstead o% using the graph to fnd the %o!a& &ength it is possi)&e to use the

e.uation +(,+-(,u(,f ,' 8sing the data !o&&e!ted !an !hange the e.uation to

(,f-(,).==3/(,/).2' This gi"es me a "a&ue o% ).(! %or the %o!a& &ength' !an do

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this %or ea!h dierent &ength and #ork out an a"erage' This is %ound in the ta)&e

)e&o#'

(,+/(,u ;ocal <ength

<'90: 0'194

<'4:1 0'194

<'90 0'192

<'9E4 0'192

<'92E 0'193

<'9:1 0'192

<'9E1 0'192

<'9E4 0'192

<'949 0'193

<'<91 0'190

This gi"es a %o!a& &ength o% 0'192' This mat!hes the "a&ue %ound %rom the graph'

(nother #a$ o% !he!king the resu&ts is to use )oth inter!epts on the graph' This

a&so ga"e me the resu&t 0'19 this sho#s m$ resu&ts #ere "a&id'

Conclusion:

;rom this data !an fnd that it #as %air&$ pre!ise as m$ per!entage error #as a&&

"er$ &o# #ith the highest at on&$ 2'<I' There #as on&$ one anoma&ous resu&t

this sho#s that the data #as %air&$ !onsistent as #e&&' 6hen the graph #as

p&otted the gradient #as meant to )e 1 ho#e"er it #as 1'01<< 0'00<' This

means that there #as a sma&& error this !ou&d )e due to the &ens not )eing

per%e!t&$ !ur"ed or the image o% the f&ament )eing diK!u&t to te&& #hen it is in%o!us' =$ data !&ear&$ sho#ed that the e.uation is ee!ti"e as ea!h pie!e o% data

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ga"e the same resu&t %or the %o!a& &ength this means that the data #as "er$

!onsistent' This resu&t a&so mat!hes the resu&t gi"en on %rom m$ graph sho#ing

that there is a !&ear &ink )et#een the e.uation and the graph produ!ed'

(s mentioned ear&ier there are 2 main errors the &a!k o% per%e!t !ur"ature and

the diK!u&t$ o% te&&ing #hen the image is in %o!us' This !ou&d ha"e ae!ted m$resu&ts )$ up to 4'3:I this is %air&$ high and there%ore shou&d )e redu!ed'

7"era&& the data o)tained #as %air&$ pre!ise )ut !ou&d )e made a &ot )etter' t

sho#ed a high simi&arit$ to the e.uation +(,+-(,u(,f , and the graph &inked to

this strong&$' The main sour!e o% error #as the s$stemati! error %rom the

!ur"ature o% the &ens' This is a pro)&em as the &ight #ou&d enter the &ens and )e

)ent in s&ight&$ dierent #a$s in ea!h part o% the &ens this #ou&d ae!t #here

the %o!a& &ength is and a&so mean that the %o!a& &ength might )e dierent %or

dierent parts o% the &ens' To impro"e the e*periment the s$stemati! error shou&d

)e redu!ed this #ou&d sho# a greater &ikeness the e.uation and )e mu!h !&oser

to the true "a&ue'

Improvements:

*nitial e0periment errors

;or m$ initia& e*periment %ound that m$ &argest errors #ere a s$stemati! error

and a random error' The s$stemati! error #as !aused )e!ause the &ens #asn,t

per%e!t&$ !ur"ed so the &ight #ou&dn,t %o!us in the same #a$ ea!h time' The

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random error #as !aused )e!ause the image o% the f&ament #as hard to te&&

#hen it #as in %o!us'

Reducing the errors

;or the s$stemati! error !o"ered part o% the &ens #ith tape so that on&$ the

!entre &et an$ &ight through' This #ou&d mean that the !ur"ature o% the &ens

#ou&d )e mu!h more e"en as there #ou&d on&$ )e a portion o% it sho#ing'

;or the random error used the head o% a pin instead o% a f&ament )u&) as the

pin has mu!h more detai& and there%ore is a &ot easier to te&& #hen the image is in

%o!us'

Doing this )rings the error o% the distan!e %rom the &ens to the image do#n to

0'002m'

>e? method

$1uipment:

=eter ru&er

G&ass on"e* >ens

Tape

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ork

Pin

Desk &amp

(djusta)&e )&o!k

;i*ed )&o!k

Diagram:

etting up the e1uipment.

@et up the e.uipment as sho#n in the diagram'

he e0periment.

1' Put the tape on the &ens so on&$ a 2!m diameter se!tion &ets &ight through

in the !entre o% the &ens'2' Position the &ens 20!m a#a$ %rom the pin and mo"e the s!reen so that the

image !omes into %o!us' ?e!ord the distan!e %rom the image to the &ens inthe ta)&e'

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3' =o"e the &ens )a!k 9!m and mo"e the s!reen so that the image is in %o!us

again' ?e!ord the distan!e %rom the image to the &ens in the ta)&e'4' ?epeat step 2 unti& there are 10 dierent resu&ts'9' ?epeat step 1 2 and 3 unti& there are 9 dierent resu&ts %or e"er$

measurement'

<' ;ind the a"erage "a&ue %or ea!h &ength'' Ae*t #ork out the %o!a& &ength %or ea!h dierent resu&t' To #ork out the

%o!a& &ength the e.uation is 1/"1/uC1/% or 1/"-1/u1/%'

u is the o)je!t distan!e the distan!e %rom the &ens to the o)je!t this is

a&#a$s negati"e

" is the image distan!e the distan!e o% the s!reen %rom the &ens #hen the

image is in %o!us

% is the %o!a& &ength this is #hat #e,re tr$ing to fnd'

$rrors.

There !ou&d )e a sma&& s$stemati! error in the distan!e %rom the &ens as the ru&er

on&$ measures in mm so there !ou&d )e up to a 0'9mm error'

Results:

Distance from the lens to theo56ect 7m8 9).))(

Distance from the lens to the image7m8 9 ).))2

est ( est 2 est 3 est est !

-0'200 0'<< 0'<:9 0'< 0'<:0 0'<:3

-0'290 0'401 0'3E 0'404 0'401 0'403

-0'300 0'322 0'31E 0'323 0'323 0'321

-0'390 0'2:1 0'2 0'2:0 0'2:0 0'2E

-0'400 0'299 0'294 0'291 0'294 0'292-0'490 0'239 0'23: 0'23 0'23: 0'23E

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-0'900 0'22 0'229 0'22< 0'224 0'229

-0'990 0'21 0'21 0'214 0'21< 0'21<

-0'<00 0'210 0'20E 0'20: 0'211 0'210

-0'<90 0'203 0'209 0'204 0'209 0'204

Date14/02/20

14

14/02/20

14

14/02/20

14

14/02/20

14

14/02/20

14

This !&ear&$ sho#s that there #ere no anoma&ous resu&ts as a&& the data is

!on!ordent #ith ea!h other'

$rror analysis

Distance from thelens to the o56ect

7m8 9).))2

Distance from the lens to theimage 7m8 9 ).))!

est(

est2

est3

est

est!

A+erage

Range

pread

-0'200 0'<< 0'<:9 0'< 0'<:0 0'<:30'<:0

0'00E

0'0049

0'

-0'290 0'401 0'3E 0'404 0'401 0'4030'401

0'00< 0'003

0'

-0'300 0'322 0'31E 0'323 0'323 0'3210'322

0'004 0'002

0'<

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-0'390 0'2:1 0'2 0'2:0 0'2:0 0'2E0'2E

0'004 0'002

0'

-0'400 0'299 0'294 0'291 0'294 0'2920'293

0'004 0'002

0':

-0'490 0'239 0'23: 0'23 0'23: 0'23E

0'23

0'00

4 0'002

0'

:-0'900 0'22 0'229 0'22< 0'224 0'229

0'2290'00

30'001

90'

-0'990 0'21 0'21 0'214 0'21< 0'21<0'21<

0'003

0'0019

0'

-0'<00 0'210 0'20E 0'20: 0'211 0'2100'210

0'003

0'0019

0'

-0'<90 0'203 0'209 0'204 0'209 0'2040'204

0'002 0'001

0'9

;ormu&a %or per!entage error Fma*-min/a"erage * 100

1< | P a g e

1/Distan!e %rom the&ens to the o)je!t m-

1 0'002

1/Distan!e %rom the&ens to the image

m-1 0'009

-9'000 1'41

-4'000 2'43E

-3'333 3'10<

-2':9 3'9:4

-2'900 3'E93

-2'222 4'21E

-2'000 4'444

-1':1: 4'<30

-1'<< 4'<2

-1'93: 4'E02

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"raphs:

7n graph $ p&ots are 1/image distan!e

* p&ots are 1/o)je!t distan!e

$ inter!ept is 1/positi"e %o!a& &ength

* inter!ept is 1/negati"e %o!a& &ength

Anomalies and $rrors:

Anomalies: had no anoma&ous resu&ts'

$rrors: =$ data is !&ear&$ repeata)&e as the ma*imum per!entage error is on&$0':I' This means that m$ data is "er$ !onsistent and is repeata)&e' =$ gradient

1 | P a g e

$0'EE4*C<'42:

H nter!ept <'42: 0'09 0'I m-1J nter!ept -<'4E9 0'1 1'9I m-1

("erage nter!ept <'4<31 0'09

1'1<I m-1

7/18/2019 mxm



is not one this is #hat it shou&d )e ho#e"er it is on&$ 0'00< o' This is neg&igi)&e

and #ou&d not ae!t the resu&t in a %undamenta& #a$'

Analysis:

=$ graph sho#s that the $ interse!t is <'42: and m$ * interse!t is -<'4E9' This

gi"es me an a"erage "a&ue %or 1/% o% <'4<13 #ith a per!entage error o% 0'01I'

This means that the %o!a& &ength is 1/<'42: or 0'199< #ith the same per!entage

error'

;ocal <ength of lens: ).(!!=m ).)(

&onclusion:

7"era&& %ound that m$ se!ond e*periment great&$ impro"ed upon the initia&

e*periment as the per!entage error redu!ed )$ 4'0EI and the resu&ts #ere

mu!h more !onsistent #ith ea!h other' t !&ear&$ sho#s that the %o!a& &ength is

re&ated to the distan!e )et#een the o)je!t and the &ens and the &ens and theo)je!t this a&&o#ed me to !a&!u&ate the %o!a& &ength o% the &ens "er$ a!!urate&$

#ith minima& error' n the ta)&e )e&o# the t#o e*periments are !ompared the

gradient %or )oth &ines shou&d )e 1 the gradient %or the se!ond e*periment is

on&$ 0'00< o #hereas the frst e*periment e*periment #as 0'01 o #hi!h

means that the se!ond e*periment massi"e&$ impro"ed on the frst' =$

p&us/minus error a&so redu!ed )$ o"er 90I %rom the frst to the se!ond

e*periment'

$0periment ;ocal <ength "radient

$0periment ( 0'192 0'009 1'01 0'02

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