Lab 10 thin lenses PDF

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LAB 10: THIN LENSES Group #: Analyst Name: SAMPLE CALCULATIONS Show the following calculations: Use the information from the graph’s trendline equation to show the following calculations: The focal length 1 1 f= = =10.28 cm b 0.0973 The percent uncertainty in the focal length 1 f= b −1 ∂ f −1 = 2= =−105.6 ∂b b (0.0973 )2 δf =

√(

∆f=

)

2

∂ f ( )2 = δb ∂b

√ ( 105.6 ) ( 4.5 ×10 2

) =4.752 × 10−2 cm

−4 2

δf ×100 =4.6 % f

The percent error −accepted | measured |×100=|10.2810.0−10.0 |×100=2.8 % accepted

PE=

For the object distance of approximately 15 cm, show the following calculations: Using image and object heights: The lateral magnification: hi −7.952 m= = =−1.940 h0 4.100 Uncertainty in the lateral magnification: Lab 10: THIN LENSES

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h m= hi

o

1 ∂m 1 = = =0.2439 ∂ hi ho 4.100 ∂ m −hi −−7.952 = =0.4731 = ∂h o h2o ( 4.100 ) 2

√(

δm=

Δ m=

)

( )

∂m 2 ∂m 2 2 2 2 2 2 δ hi ) + δ ho ) = √( 0.2439) ( 0.001 ) + ( 0.4731 ) ( 0.001 )2=5.323 × 10−4 ( ( ∂ hi ∂ ho

δm 5.323 ×10−4 −2 =2.7 ×10 % ×100= 1.940 m

Using image and object distances: The lateral magnification: −i 29.31 m= = =−1.954 p 15.0 Percent Uncertainty in the lateral magnification: −i m= p ∂m −1 −1 = = =−0.0666 p 15.0 ∂i 29.31 ∂m i = 2= =0.1303 ∂ p p ( 15.0 )2

√(

δm=

)

2

( )

2

∂m ∂m 2 −3 2 2 2 2 2 ( δi ) + ( δp ) = √ (−0.0666 ) (0.05 ) +( 0.1303 ) ( 0.05) =7.317 × 10 ∂i ∂p −3

Δ m=

7.317 ×10 δm ×100= m 1.954

=0.37 %

Percent Difference in the obtained lateral magnifications

|

PD=

|

1.954 −1.940 ×100=0.72 % 1.954 +1.940 2

Lab 10: THIN LENSES

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Use the data from the double biconvex lens scenario (steps 9 and 10 of the lab procedure) to show the following calculations for each lens: The focal length p1 i1 ( 16.70 ×31.50 ) = f 1= =10.91 cm i 1 + p1 (31.50+16.70) f 2=

p2 i2 ( 34.78 × 50.50 ) =20.60 cm = i 2 + p2 (50.50+34.78)

The uncertainty in the focal length 2 2 ∂f1 − p1 −( 16.70) = =−0.120 = ∂ i1 ( i1 + p1)2 (31.50+ 16.70 )2 2

2

i1 ∂f1 (31.50 ) = =0.427 = 2 ∂ p1 ( i 1+ p1 ) ( 31.50 + 16.70 )2

√( )

2

δf =

∆ f 1=

( )

2

∂f 1 ∂f1 2 2 δ i1 ) + δ p1 ) = ( ( ∂i1 ∂ p1

√ ( −0.120)

2

2

2

2

( 0.05 ) +( 0.427 ) ( 0.05 )

= 0.0222 cm

δf1 ×100=0.20 % f1

34.78 ¿ ¿ ¿2 ¿ − p 22

∂f2 = =−¿ ∂ i2 ( i2 −p 2 ) 2 2 i22 ( 50.50) ∂f1 = = =3.21 ∂ p1 ( i 2− p2 ) 2 ( 50.50 −34.78) 2

Lab 10: THIN LENSES

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2

δf =

2

∂f 2 ∂f2 2 2 δ i2 ) + δ p 2) = ( ( ∂i2 ∂ p2

√( )

∆ f 2=

( )

√ ( −2.21) ( 0.05 ) +( 3.21) ( 0.05) 2

2

2

2

= 0.195 cm

δf2 ×100=0.95 % f2

The percent error −accepted 10.91−10.0 ×100=| × 100= 9.1% | measured | accepted 10.0 |

PE1=

−accepted −20.0 | measured |×100=| 20.620.0 |×100=3.0 % accepted

PE2=

Lab 10: THIN LENSES

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TABLE OF RESULTS EXPERIMENTAL FOCAL LENGTH

10.28

f ±∆ f

4.6 %

PERCENT ERROR

2.8 %

PE (%)

LATERAL MAGNIFICATION

LATERAL MAGNIFICATION

m1 ± ∆ m1

m2 ± ∆ m2

PERCENT DIFFERENCE PD

−¿ 1.940

±

2.7 ×10 %

−¿ 1.01 2

±

3.4 ×10 %

−¿ 0.69 70

±

−¿ 0.50 98

±

−¿ 0.39 51

±

−¿ 0.34 00

±

−¿ 0.33 66 Lab 10: THIN LENSES

±

−2

−1.954

−2

−1.00

4.3 ×10

−2

−0.6840

% 5.4 ×10

−2

% −2

1.0 ×10 %

7.6 ×10−2

% 7.4 ×10−2

−0.5103

−0.4042 −0.3388 −0.2913

( %)

± 0.37% ±

0.72

0.35%

1.2

0.34%

1.9

0.37%

0.10

0.38%

2.3

0.40%

0.35

± 0.41%

14.0

±

±

± ±

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% −¿ 0.25 61

±

9.8 ×10−2

%

−0.2558

±

0.15%

0.12

TABLE OF RESULTS – TWO LENS SYSTEM (Step 9&10) FOCAL LENGTH – FIRST LENS f 1 ± ∆ f 1(cm)

10.91

±

0.22 %

FIRST LENS PERCENT ERROR 9.1 %

PE ( % ) FOCAL LENGTH – SECOND LENS

20.60

±

0.95%

f 2 ± ∆ f 2(cm) SECOND LENS PERCENT ERROR 3.0 %

PE

( %

Lab 10: THIN LENSES

)

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