第六章
1.Design an aplanatic lens with r
1
=-95mm, object is at the center of first surface, second spherical surface satisfies aplanatic condition. If the lens thickness d=5mm,index n=1.5,and lens is in air, find:
1) the second radius of the lens,
2) the lens magnification solution:
(1)first surface:

1
 n
1 n
1
'

1
1 .
5 ； second surface : L
2

( n
2
 n
2
' ) r
2
/ n
2
； L
2
'

( n
2
 n
2
' ) r
2
/ n
2
'
L
2

L
1
'
 d
 
100 mm , n
2

1 .
5 , n
2
'

1 r
2
 
60 mm
（2
  
1

2

2
 n
2
L
2 n
2
' L
2
'

( n
2 n
2
'
)
2 
(
1 .
5
1
)
2
 
1 .
5
2.what does mean by aplanatic imaging? what does mean by isoplanatic imaging? If an object is in the vertical plane cross the each of tree aplanatic points, can the refractive surface forms a perfect image of the object?
3.if the primary tangential coma of an optical system is equal

to width of focus (

/ n ' u ' ) ,what is

S
II
Solution:
K
T
'
 
3
2 n ' u '

S
II

S
II

2

= 3
4. if the primary spherical aberration of an optical system is equal to depth of focus (

/ n ' u '
2
) ,what is

S
I
?
Solution:

L '
 
1
2 n ' u '
2

S
I

S
I
= 
2

5.if an object is at the vertex of the lens, second surface satisfies aplanatic condition, set lens index n=1.5，thickness d=4,find the angular magnification and r
2
?
Solution:

1

1 ；
L
2

( n
2
 n
2
' ) r
2
/ n
2
； L
2
'

( n
2
 n
2
' ) r
2
/ n
2
'
L
2

L
1
'
 d
 
4 mm , n
2

1 .
5 , n
2
'

1 r
2
 
2 .
4 mm
  
1

2

2
 n
2
L
2
' n
2
' L
2

( n
2 n
2
'
)
2 
(
1 .
5
1
)
2
 
2 .
25 ；
 
1


0 .
44
6.lHow many spherical aberration free points are there in a spherical mirror?
7.design a achromatic telescope with cemented doublet, f ' =100mm， K9( n
D
=1.5163，
D
=64.1)and F2( n
D
=1.6128，
D
=36.9)，

I if positive lens r
1
 r
2
，find
(1)the focal length of positive and negative lenses,
(2)tree radius.
Solution:
(1)


1
 
1
/

1

 
2

2
/

2

0 f '
1

42 .
4 mm ; f '
2
 
73 .
7 mm

1
（2）

2


( n
1
( n
2

1 )(

1

1 )(

2



2
)

3
) r
1
 r
2
， n
1

1 .
5163 , n
2

1 .
6128 r
1
  r
2

43 .
78 mm , r
3
 
1429 .
3 mm
8. in fig.6-22, point out
(1)marginal spherical aberration

L
' m
=?
0
(2) 0.707 zone spherical aberration

L
'
0 .
707
=?
-0.03
(3) marginal chromatic aberration

L
'
FC
=?
0.06
(4) paraxial chromatic aberration
 l '
FC
=?
-0.06
(5) 0.707 zone chromatic aberration

L
'
FC 0 .
707
=?
0
(6)chromatic aberration

L
'
FC
=?
0.12
(7)secondary spectrum

L
'
FCD
=?
0.07

9.fesign a cemented doublet lens with f ' =100mm，the glasses are
K9( n
D
=1.5163,

D
=64.1) and F2( n
D
=1.6725,

D
=32.2)，in order to compensate chromatic aberration of other element, the lens should reserve primary longitudinal chromatic aberration
 l
'
FC
=-0.26mm, find
(1)the power of positive and negative lenses
(2)How large is the secondary spectrum of the lens.
solution：
（1）
 l '
FC
  n ' k
1 u '
2 k k 
1 h
2



0 .
26
  h u ' 2 k
2 k 
1


 
4 f '
2

(

1



2
)
  
1
 
2

1
 
1

2
0 .
065
 2

2
 
 
1
/

2
 f '
1

50 .
83 mm

1
  
1

2
0 .
065
 2

2
 
 
1
/

1
 f '
2
 
103 .
38 mm
（2）

L '
FCD

0 .
00052 f '

0 .
052 mm
10.a cemented doublet lens with f ' =100mm，D/f,=1∶5，if the lens has only primary aberration, the aberration coefficient of marginal ray are respectively
1 2 3
S
I
： 0.0100104 -0.0338527 0.0256263 find：1)How large is primary spherical aberration of the lens?

2) if primary spherical aberration is less than 4 times of depth of focus, does the aberration satisfy the tolerance of the lens?
3) How large is the secondary spectrum of the lens? solution：
1）

L ' u '
3
( 初）  
1
2 n
' k u '
2 k
 arctg 0 .
1 k 
1
S
I

L ' ( 初） 
0 .
08979 mm
2)
4
 n ' u ' 2 m

0 .
223479 mm
﹥ 0.08979mm, satisfy the tolerance of the lens
3)

L '
FCD

0 .
00052 f '

0 .
052 mm
11.what called Petzval field curvature? What method can be used to correct field curvature? If the aberration of astigmatism is corrected, does the field curvature is corrected simultaneously? solution：for thin lens system, with separated positive and negative lens, make

 n

0
；or meniscus thick lens， if astigmatism is corrected , the field curvature is still present。
12. what is the function of field lens? What is the characters of field lens? Why ?

solution： reduce the aperture of the lenses of following it, change the position of exit pupil。
Because field lens is coincided with image plane, without aberration except positive 由于场镜与像平面重合，
故除产生正场曲和由此衍生的正畸变外，不产生其它像差。
13.a thin lens is placed at the center of a spherical surface, the two radius of the lens are same, aperture stop is coincide with the lens. if abject is at infinity ，analyze the image character of the system。 solution：
（1）for meniscus r
1 r
2
S
IV

0
 
( n

1 )(
1 r
1

1 r
2
)

0

Because of thin lens， S
V
S
III
C
I


J
2

 h
2


0
/
 
0

C
II

0
Residual aberrations are S
I
、 S
II
（2）for spherical mirror
Stop at center， i z

0

S
II

S
III

S
V

0
Mirror reflection,

C
I

C
II

0
Residual aberrations are S
I
、 S
IV
（3）for system,， S
I can be compensated，

Residual aberrations
S
II

JW S
IV

2 J
2 r
14. the curve of off axis aberration is shown in fig.6-23，
Find ： K t
'
, X t
'
, x t
'
,

L
'
T
(off axis S.A.) and distortion
 y
' z
。
（ K t
'  
0 .
1 X t
' 
0 , x t
' 
0
 y z
' 
B '
0
B ' z
）
15. a symmetrical optical system withβ=-1 时，how large are the vertical aberration and longitudinal aberration? solution：vertical aberrations are zero, longitudinal aberration are two times of half system.
16.in panoramic sight scope, how is the characters of head rectangle prism and Dove prism? How is the aberration of the bottom roof rectangle prism? Are there any relation with distance to objective lens?

solution：head rectangle prism and Dove prism are in parallel light beam, without aberrations，bottom roof rectangle prism has all of aberration except field curvature. No matter how far is it from the lens.
17. in all of seven primary aberration, which aberration effects the image sharpness? which aberration does not effects the image sharpness? Which aberration is only depend on aperture? Which aberration is only depended on field? Which aberration is only depended on aperture and field?
Solution: distortion;
S.A> and chromatic aberration are depended on only aperture ； astigmatism 、 field curvature 、 distortion and transverse chromatic aberration are depended on field；came is depended on both field and aperture。
18. distortion can be written as ：
 y '
 cy '
3
，
 z '

0 ，what is relative distortion?
how large is transverse magnification？
Solution: ,
19. a thin cemented doublet, if
C
I
=0, how is
C
II
=? If the

lens is separated doublet, how is the chromatic aberration?
solution: 0,
C
II is not zero
20．a cemented doublet with positive power, and is composed of positive lens and negative lens ，which lens uses K glass, and which uses F glass? why?
Solution: positive uses K glas, negative uses F glass
21. correct spherical aberration is at marginal zone, why does longitudinal chromatic aberration correction is at
0.707
h m
?
Solution: make both paraxial and marginal longitudinal chromatic aberration small，equal and opposite
22．How can you prove that meridional and sagittal focal lines are separated？And why meridional focal line is in front of sagittal focal line?
See Yong equation
23. in object plane there is five points A、B、C、D、E，shown in Fig.（a）； after optical system, the image of A is like
A’， Fig.(b)。 how about the other image of B、C、D、E？

C confusion circle ，B、D、E are coma ， head is outward
24 A“米”wheel is at the front of optical system， the lens has astigmatism。How is the wheel image in Gauss plane？ How is the wheel image in meridional plane？How is the wheel image in sagittal plane？
Gauss meridional sagittal
25．Compare with Lister microscope objective，how many times
NA of Amich and Abbe microscope objective is increased？
Solution Amich n
1
2 ,
Abbe n
1
2 n
2
26．Judge what aberration are there in following Fig.？ what relation is between meridional and sagittal plane？and how large is it（注 ZEMAX 中 EY、EX 分别表示子午面和弧矢面的横向

像差，PY、PX 分别表示子午面和弧矢面的入瞳半径 ）
Solution: astigmatism , 3 times
27．Judge how is the secondary spectrum in following Fig.？ how large is paraxial chromatic aberration ?
Solution : 0.55h
m
， 0.85h
m
， 0.06mm
26 题图 27 题图
28．In ZEMAX program there is no the curve of coma, how can you judge the coma in ZEMAX？
Ray, spot