chapter 4 thin lenses
TRANSCRIPT
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
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)
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
Image Formation
All relevant rays from one point (object) go to
another point (image)
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
Sign convention
• All from left to right
• Up is positive for object and image dimensions
Left Right
s + -s + -
s’ - +
f + -
f’ - +
r - +
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’
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
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’
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
Lateral magnification
' ' '
' ' '
M Q A M
M Q A M
y M Q
y M Q
=
==
' 'y sm
y s= = −
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
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
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.
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
+ =
= −
+ =
Thin lens combinations-parallel rays
Thin lens combinations-oblique rays
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.
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)
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
− + =
+ = + = +
+ = + =
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
Exercises
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+ =