应用光学第六章-英文习题

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: 5

.11'111==

n n β；

second surface : 22222/)'(n r n n L +=；'/)'('22222n r n n L +=

1',5.1,100'2212==-=-=n n mm d L L

mm r 602-= （2 21βββ=

2

22222222)1

5

.1()'(''===

n n L n L n β

5.1=β

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 )''/(u n λ,what is ∑II S

Solution:

II T S u n K ∑-

=''23' ∑II S =32λ-

4. if the primary spherical aberration of an optical system

is equal to depth of focus

)''/(2

u n λ,what is ∑I S ? Solution:

∑-

=I

S

u n L 2

''21

'（初）δ ∑I S =λ2-

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: 11=β；

22222/)'(n r n n L +=；'/)'('22222n r n n L +=

1',5.1,4'2212==-=-=n n mm d L L

mm r 4.22-=

21βββ=

2

22222222)1

5

.1()'(''===

n n L n L n β 25.2=β；

44

.01

==

β

γ

6.lHow many spherical aberration free points are there in a spherical mirror?

7.design a achromatic telescope with cemented doublet,

'f =100mm ， K9(D n =1.5163，D ν=64.1)and F2(D n =1.6128，

D ν=36.9)，

I if positive lens 21r r =，find

(1)the focal length of positive and negative lenses,

(2)tree radius. Solution:

(1) 0//22112

1=Φ+ΦΦ+Φ=Φνν mm f mm f 7.73';4.42'21-==

（2）))(1()

)(1(32222111ρρρρ--=Φ--=Φn n 21r r =，6128.1,5163.121==n n

mm r mm r r 3.1429,78.43321-==-=

8. in fig.6-22, point out

(1)marginal spherical aberration

'm

L δ =?

0 (2) 0.707 zone spherical aberration '707

.0L δ=?

-0.03 (3) marginal chromatic aberration 'FC

L ∆ =?

0.06 (4) paraxial chromatic aberration

'FC

l ∆=?

-0.06 (5) 0.707 zone chromatic aberration '707

.0FC L ∆=?

(6)chromatic aberration 'FC

L δ=?0.12 (7)secondary spectrum 'FCD

L ∆=?

0.07