chapter 4 thin lenses
TRANSCRIPT
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Homework for chapters 4 and 5
• Chapter 4: 3, 4, 8, 12, 13, 14, 16
• Chapter 5: 3, 4, 5, 6, 11, 12, 15,16
• Due next Tuesday before class
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Thin Lenses and Their Foci
How thin is thin?
When thickness << all
relevant distances
Primary foci Fs
Secondary foci F’s
Focal lengths
f=f’ for thin lenses
In air (uniform medium)
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Focal plane and chief ray
• Parallel rays are
focused at the focal
plane
• Chief ray does not • Chief ray does not
deflect in thin lenses
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Image Formation
All relevant rays from one point (object) go to
another point (image)
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Conjugate points and planesTo find an image
1. By graph
2. By experiment
3. By calculation
Lens formula
1 1 1
's s f+ =
Equivalent of Gaussian equation
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Sign convention
• All from left to right
• Up is positive for object and image dimensions
Left Right
s + -s + -
s’ - +
f + -
f’ - +
r - +
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Graphical-parallel rays
• 4//1, refraction goes through F’
• 5 is the chief ray
• 6 goes through F, refraction parallel to 1
• 4, 5, and 6 meet at Q’
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Graphical-parallel rays 2
• 4//1, refraction 5 imaginably goes through F’
• 6 imaginably goes through F, refraction 7
parallel to 1
• 8 is the chief ray
• 5,6 and 8 meet at Q’, virtual image
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Graphical-oblique ray
• Arbitrary ray 3 from object M meets lens at R
• Chief ray 5//3
• 5 meets secondary focal plane at X
• 6 goes through T and X and meets 1 at M’
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Lens Formula
s=6.0 cm, f=4.0 cm, what is s’?
1 1 1
's s f+ = '
sfs
s f=
−
s’=+12.0 cm can be checked easily by the graphical method
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Lateral magnification
' ' '
' ' '
M Q A M
M Q A M
y M Q
y M Q
=
==
' 'y sm
y s= = −
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Virtual Images
s=6.0 cm, f=10.0 cm, what is s’&m? s=12.0 cm, f=-6.0 cm, what is s’&m?
6 10' 15
6 10
' 152.5
6
sfs cm
s f
sm
s
= = = −− −
−= − = − = +
i 12 ( 6)' 4.0
12 ( 6)
' 4 1
12 3
sfs cm
s f
sm
s
−= = = −− − −
−= − = − = +
i
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Lens Maker’s equation
1 1 ( 1)
1 1' 12 1'
1 1 (1 )
n
s s rs s
n
−+ =
= −−
1 2
1 1 1( 1)( )
1 1 1
nf r r
= − −
+ =
1 2 1 2
1 1 (1 )
1' 2 ' 21 1 1 1
( 1)( )'
n
s s r
ns s r r
−+ =−
+ = − −
1 1 1
's s f+ =
Gaussian form of lens formula
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Lens Maker’s equation-an example
1 2
1 1 1( 1)( )n
f r r= − −
Want to make plano-convex
lens f=25.0 cm. Glass has
n=1.520, find radius of
curvature.
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Thin lens combinations-by formulae
1 1 1
1 1 1
2 1
2 2 2
1 1 1
'
If the distance between lenses is
'
1 1 1
'
s s f
d
s d s
s s f
+ =
= −
+ =
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Thin lens combinations-parallel rays
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Thin lens combinations-oblique rays
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Object space and image space
Both spaces occupy the whole space
All rays from the object occupy the object space
All rays forming the image occupy image space
4 is in the object space
7 is in the image space of the 1st lens but in the object space of the 2nd lens
M1’ is in the image space of lens 1 and the object space of lens 2
10 is in the image space of the second lens.
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Power of thin lenses
1 2
1 1 1( 1)( )P n
f r r= = − −
Measured in diopters (number when f is measured in meters)
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Thin lens in contact
1 1 1
2 1 1
1 1 1
'
If the distance between lenses is 0
' '
1 1 1
s s f
d
s d s s
+ =
== − = −
− + =1 2 2
1 21 2 1 2
1 2
1 1 1
' '
1 1 1 1
'
1 1 1 1 1
'
s s f
P Ps s f f
s s f f f
− + =
+ = + = +
+ = + =
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Lens Formula-Newtonian
2
'
'
'
'
y y
x f
y y
x f
xx f
−=
−=
=
Hyperbolic equation
Both negative or both positive
Careful with negative f
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Exercises
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Lens makers formula-3 media
1 1 1
' ( ' )
'
' '' ( '' ')
' ''
n n n n
s s r
n n n n
s s r
−+ =
−+ =2 2 2
2 1
1 2 1 2
' ''
' '
We thus have
'' ( ' ) ( '' ')
''
s s r
s s
n n n n n n
s s r r
+ =
= −
− −+ = +
1 2
1 2
Define
'' ( ' ) ( '' ')
''
We have
''
''
If n=n'', then
n n n n n n
f f r r
n n n
s s f
− −= = +
+ =
1 2
1 1 1
s s f+ =