第10章 几何光学

v = v2 v1 = u 2
1 u

1 v
n2 n1 1 1 r n1 r2 1
1 1 r r 2 1
1
1 u

1 v

1 f
n2 n1 f n1
Gauss Equation about thin-lens
1屈光度 = 100度
24
薄透镜
. 单向放大率 （复习内容） (lateral magnification)
A
F
B
•
O •
F
B
A
1 1 f ( n 1) r r 2 1
1

凸球面对着入射光线，r取正号 Sign convention： 凹球面对着入射光线，r取负号
22
薄透镜
1 1 f ( n 1) r r 2 1
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Principal quantity about thin lens
Focal length
n2 n1 f n1 1 1 r r 2 1
1
薄透镜

n1 = 1 , in the air n represents the refractive index of the material of thin lens , then the focal length
System
球面折射系统
If a optical system is made up of many refractive spherical surface ，and all the center of curvature of refractive surface is on a line ，then we call the system is coaxial system .The line which joins all the center of curvature is called principal optic axis .
n1 n2 r2



+
n1 u

n1 v

n2 n1 r1

n1
u = u1
v = v2 v1 = u 2
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n1 u

Байду номын сангаас

n2 v1

n2 n1 r1
薄透镜
n1 u = u1
n1 n2 r2
n2 n1
n2 v1

n1 v

n1 n2 r2
+
n1 u

n1 v

n2 n1 r1
4
球面折射系统
1.Refraction at a Spherical Surface
analyze
object
n1 • u
i1 A i 2

r
P
• C v

n2 •
image
n1 sin i1 n2 sin i2 i1
i2 i2

AP u

几 何 光 学 的 理 论 基 础
反射和折射定律 光的独立传播定律 光 的 直 线 传 播 定 律
几何光学是以光的直线传播性质为基础， 研究光在透明介质中传播规律的学科。
1
Section 1. Refraction at a Spherical Surfa
Section 2. The lens
Section 3. The eye
n1 u n2 v n2 n1 r
球面折射系统
We adopt the following rules： 1、When the object is on the same side of the
Paraxial beam refracting surface as the incoming light ,the object distance u is positive ;otherwise it is negative. 2、When the image is on the same side of the refracting surface as the outgoing light ,the image distance v is positive ;otherwise it is negative. 6
2 . Coaxial System
3
球面折射系统
1.Refraction at a spherical surface
system n1
object
• u
Object distance
r
n2
•C •
image
v
Image distance
law
n1 u n2 v n2 n1 r
refractive index radius of curvature
8
球面折射系统
secondary focal point n1 n2 r F2
•C
n1 u

n2 v

n2 n1 r
f2 secondary focal length
f2 n2 n2 n1 r
9
n1

n2 f2

n2 n1 r
球面折射系统
focus Primary focal point Primary focal length Secondary focal point Secondary focal length
1 1 r r 2 1
1
Form
n1 u n2 v n2 n1 r


u
可得
n2 n1 f n1
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薄透镜
n1 u n2 v1
n2 v1 n1 v

n2 n1 r1
n1 n2 r2
To the first refractive surface To the second refractive surface
5 . Lens Aberrations
16
1. The thin -lens Equation
Lens
Be made up of two coaxial refractive surface Including(converging lens and diverging lens)
薄透镜
Two refractive surface are all spherical surfaces ,or one is spherical surface ,another one is plane。 The distance on the optic axis between the two refractive surface is lens thickness Thin lens Thick lens
1
Converging lens
Diverging lens
r1 > 0
r2 < 0
f>0
r1 < 0
r2 > 0
f<0
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薄透镜
Dioptric power

1 f

表示透镜的折光本领 D越大，系统的折光能力越强

unit：diopter (屈光度） 通常所说的眼镜的度数等于屈光度的1/100倍
1 .5 40

1 .0 v2

v 2 ＝11.4cm
15
Section 2 The lens
1. The Thin --lens Equation
2. The Combination of the thin lens 3 . The Thick lens
4 . The cylindrical lens
11
2 . Coaxial system
Applying the methods of single spherical refraction in turn,the object for the second surface being the image formed by the first.
AP v

AP r
n1 u n1 u

n1 r n2 v

n2 r

n2 v
n1 ( ) n2 ( )
n2 n1 r
5
Paraxial condition, i1 i2
1.Refraction at a Spherical Surface
discuss
Condition：
12
2 . Coaxial system
Analyze
球面折射系统
光线经前一个折射面所成的像，是下一个 折射面的物，对于系统中的多个折射面，如此 依次成像，即可得到最后的像。
Attention


前一像作为下一折射面的物时，是实 物(real object )还是虚物(virtual object) 仍对近轴光线成立
Section 4. The Magnifier and Microscope
Section 5. The Special Microscope and Fibers
2
Section 1. Refraction at a Spherical Surfa
1 . Refraction at a Spherical Surface
13
Example
A glass ball(n=1.5)which diameters is 20cm .A object is put at the place of 40cm before the sphere .Where is the image ?
To the first refractive surface
3). The light rays through focal point is parallel with the Axis after refraction。
F
•
O
F
•
•
18
Imaging equation about thin lens
n1
n2
薄透镜
u = u1
v = v2
1 1 v 1 f
n1＝1.0，n2＝1.5，u1＝40cm，r＝10cm，
1 .0 40 1 .5 v1 1 .5 1 .0 10
v 1＝60cm
14
To the second refractive surface
u2＝－（60-20）＝－40cm，n1＝1.5，n2＝1.0，r＝－10cm，
1 .0 1 .5 10
n1 u n2 v n2 n1 r


n 2 n1 r
(D) Dioptric power
A quantity of describing the ability of refraction For the refractive system : (diopter)
R: meters
The lens thickness is negligible in comparison with the object distance and the image distance
17
Basic imaging law about thin lens
薄透镜
1). The lines through the center of the lens don’t change direction . 2) . The parallel light lays with the axis pass through the focal point after refraction；
7
1.Refraction at a Spherical Surface
n1 u n2 v n2 n1 r
Primary focal point F1
n1
r •C
•
n2
f1 Primary focal length
n1 f1 n2 n2 n1 r f1 n1 n2 n1 r
n 2 n1 r
n1 f1 n2 f2
Image is at the infinity
f1 n1 n2 n1 r
Object is at the infinity
f2 n2 n2 n1 r
Focal degree
(diopter--D)
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2 . Coaxial system
1.Refraction at a spherical surface
3、When the center of curvature C is on the same side as the outgoing light ,the radius of curvature is positive ;otherwise it is negative.