chapter 5 thick lenses

7/30/2019 Chapter 5 Thick Lenses

1/27

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


2/27

Lens makers formula-3 media

1 1 1

' ( ' )

'

' '' ( '' ')

n n n n

s s r

n n n n

+ =

+ =

2 2 2

2 1

1 2 1 2

' '

We thus have

'' ( ' ) ( '' ')

''

s s rs 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 nP

f f r r

n n n n

s s f f

= = = +

+ = =

1 1 1

''s s f

+ =


3/27

Thick lens as two spherical surfaces

1 1 1

' ( ' )'

n n n ns s r

+ =

2 1 2 1' 's A A s=

2 2 2

' '' ( '' ')' ''

n n n ns s r

+ =


4/27

Thick lens example

Equiconvex lens r =-r =2 cm, n=1.00, n=1.50, n=1.33, s1=5 cm

from A1, and A1A2=2 cm. Find s2.

1

1

2 1 2 1

1 1.50 (1.5 1)

5 ' 2

' 30 cm

' ' 28 cm

s

s

s A A s

+ =

=

= =

2

2

1.5 1.33 (1.33 1.5)

28 '' 2

'' 9.6 cm

s

s

+ =

= +


5/27

Thick lens Graphical solution


6/27

Focal points and Principal points

Principal points

fandfmeasured off H and H'' ''n f

n f

=


7/27

Principal planes can be out of the

physical lens (wiki images, H -> H)


8/27

Sign convention All from left to right

Up is positive for object and image dimensions

Left Right

-

s - +

f + -

f - +r - +

AB - +


9/27

'' ''

'' ''

''

''''

n n n n

s s f f

V V P

n sfs

s s f

+ = =

+ =

=

If n=n'', then f=f'' and

1 1 1 1

'' ''s s f f + = =


10/27

Planes of unit magnification

'' ''

'' ''

''

''''

n n n n

s s f f

V V P

n sfs

s s f

+ = =

+ =

=

If n=n'', then f=f'' and

1 1 1 1

'' ''s s f f + = =


11/27

The oblique ray method

r1=3cm, r

2=-5.0 cm, d=2.0 cm, n= 1.50, n=n=1.00

1 1 1 2 2 2

1 1 2 2

' ' ' '' '' '

and' ''

These give

f =+6.0 cm, f '=9.0 cm, f '=+15.0 cm and f ''=10.0 cm

n n n n n n n n

f f r f f r

= = = =


12/27

General thick lens formulae

' '' '' ''=

' '' ' '' ''

n n n dn n= + d

= 1 2 1 2

1

2

1

2

2

1

2

1

A F= (1 )'

A H=+

'

A F''=+ ''(1 )'

A H''= '''

df

f

df

fd

ff

df

f

1 2

1 2

2 1

2 1

'

A F= (1 )'

A H=+

'''

A F''=+ (1 )'

''A H''=

'

nn d

PP n

n dP

P nn d

PP n

n dP

P n

5.25 and 5.26 for Fs


13/27

General thick lens formulae-Principal points

1 1 2 1 1 1 1' ' ' ' 'A F A F f f d f dj

= = =

Textbook gives H derivation

5.25 and 5.26 for Fs

1 1 2 2 1

2 2 2

2 2

2 1

1 2

'

'' '' '' '' '''' '' ''or or

'' '' ''

A H''= '' Similarly A H'= ''' '

AT A T h j h f

F f H A f H AH F f j

H N A T h j h f

d df f

f f

= = =

+


14/27

The oblique ray method-Another example

r1=+1.5cm, r

2=+1.50 cm, d=2.0 cm, n=1.0, n= 1.60, n=1.30

1 1 1 2 2 2

1 1 2 2

' ' ' '' '' 'and

' ''These give

f =+2.5 cm, f '=+4.0 cm, f '=-8.0 cm and f ''=-6.5 cm

n n n n n n n n

f f r f f r

= = = =


15/27

The oblique ray method-Another example

1 1 2 2

1 2 1 2

1

f =+2.5 cm, f '=+4.0 cm, f '= 8.0 cm and f ''= 6.5 cm

' '' ''

= 0.30' '' ' ''

A F= (1 )='

n n n dn

f f f f f

df

= + =

r1=+1.5cm, r

2=+1.50 cm, d=2.0 cm, n=1.0, n= 1.60, n=1.30

2

1

2

2

1

2

1

A H=+'

A F''=+ ''(1 )='

A H''= '''

df

f

df f

df

f

=

=


16/27

Vertex Power

1 1 22

2 2 1

1

Recall

A F= (1 ) or A F= (1 )' '

''A F''=+ ''(1 ) or A F''=+ (1 )

' '

d n df P

f P n

d n df P

f P n

Thin lens of Pn

is

needed to render

the combination

zero power.

2

21

1

power or effective power''

and A F'' is called the b.f.lA F''

(1 )'

Power

A F(1

v

n

Vertexn P

Pd

Pn

Neutralizing

n PP

d

n

= =

= =

1

2

and A F is called the f.f.l

)

'

P


17/27

Special thick lenses

Left lens always positive whether nn

HH=d, right of lens for nn

Concentric lens on the right-notice C1,C2, H, and H


18/27

Nodal points Extending the incoming and

outgoing rays until they cross the

optical axis locates the nodal

points N1

and N2.

Nodal points and principal points

surrounded on both sides by thesame medium

Notice that since rays directed

toward the nodal points exit at the

same angle, the lens may berotated about either nodal point

without altering the image.

Line through C is undeviated

C


19/27

Graphical-Nodal points

s=6.0 cm, f=10.0 cm, what is s&m? s=12.0 cm, f=-6.0 cm, what is s&m?


20/27

Graphical-Nodal points

12

'' ''

'' ''

'' , ( )'' ' ''

y s HNm y s HN

and

n n d n n

HN f A N fn f n

= = +

= = +

'' ''

'' ' '

' '

'

' '

'

f FH N F

NN HH

f H F FN

= =

= =

=


21/27

Thin lens combinations-as a thick lens

A thin lens is when H and H coincide


22/27

Thin lens combinations-as a thick lens


23/27

Thin lens 1, r1=-r2=4cm,n1=1.50, thin lens 2,

r1=-r2=-6.0cm,n2=1.60, n=1,n=1.33,n=1.0

Find P, A1F,A

2F, A

1H,A

2H


24/27

Thick lens combination and other

cardinal points

Left Out


25/27

Rotating a lens about the nodal point

Rotation of a lens about its secondary nodal point shifts therefracted rays but not the image


26/27

Finding the nodal points-the nodal slide


27/27

Panoramic camera-rotation

around a nodal point-Need very smooth rotation

chapter 5 thick lenses

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