第10章 几何光学.ppt

几何光学是以光的直线传播性质为基础，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。研究光在透明介质中传播规律的学科。光光 的的 直直 线线 传传 播播 定定 律律光光 的的 独独 立立 传传 播播 定定 律律反射和折射定律反射和折射定律几几何何光光学学的的理理论论基基础础1Section 1.Refraction at a Spherical Surface Section 1.Refraction at a Spherical Surface Section 2.The lensSection 2.The lensSection 3.The eye Section 3.The eye Section 4.The Magnifier and MicroscopeSection 4.The Magnifier and MicroscopeSection 5.The Special Microscope and Section 5.The Special Microscope and FiberscopesFiberscopes21.Refraction at a Spherical Surface2.Coaxial SystemSection 1.Refraction at a Spherical Surface Section 1.Refraction at a Spherical Surface 3systemlawn1n2uvobjectimagerCr球面折射系统球面折射系统1.Refraction at a spherical surface 1.Refraction at a spherical surface Object distance Image distance refractive indexradius of curvature4n1n2uvobjectimagerCrn1i1i2APParaxial condition,i1 i2 analyze球面折射系统球面折射系统1.Refraction at a Spherical Surface 1.Refraction at a Spherical Surface 5 discussCondition：Paraxial beamWe adopt the following rules：1、When the object is on the same side of the refracting surface as the incoming light,the object distance u is positive;otherwise it is negative.球面折射系统球面折射系统1.Refraction at a Spherical Surface 1.Refraction at a Spherical Surface 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.61.Refraction at a spherical surface1.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.Dioptric power(D)R:metersA quantity of describing the ability of refraction For the refractive system :(diopter)7n1n2CrPrimary focal pointF1f1Primary focal length1.Refraction at a Spherical Surface1.Refraction at a Spherical Surface 8n1n2Crsecondary focal point F2f2 secondary focal length球面折射系统球面折射系统9focusPrimary focal pointPrimary focal length Secondary focal pointSecondary focal lengthImage is at the infinityObject is at the infinityFocal degree 球面折射系统球面折射系统(diopter-D)10System 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.球面折射系统球面折射系统2.Coaxial system112.Coaxial systemApplying the methods of single spherical refraction in turn,the object for the second surface being the image formed by the first.12Analyze 光线经前一个折射面所成的像，是下一个光线经前一个折射面所成的像，是下一个折射面的物折射面的物，对于系统中的多个折射面，如此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。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，是实前一像作为下一折射面的物时，是实物物(real object)还是虚物还是虚物(virtual object)仍对近轴光线成立仍对近轴光线成立球面折射系统球面折射系统2.Coaxial system13Example 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 n11.0，n21.5，u140cm，r10cm，60cm 14To the second refractive surface u2（60-20）40cm，n11.5，n21.0，r10cm，11.4cm151.The Thin-lens Equation2.The Combination of the thin lens3.The Thick lens4.The cylindrical lens5.Lens AberrationsSection 2 The lens Section 2 The lens 16LensBe made up of two coaxial refractive surfaceIncluding(converging lens and diverging lens)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 thicknessThin lens The lens thickness is negligible in comparison with the object distance and the image distance Thick lens薄透镜薄透镜1.The thin-lens Equation171).The lines through the center of the lens dont change direction.2).The parallel light lays with the axis pass through the focal point after refraction；3).The light rays through focal point is parallel with the Axis after refraction。FOF薄透镜薄透镜Basic imaging law about thin lens18 u=u1 v=v2 n2 n1可得可得薄透镜薄透镜Form Imaging equation about thin lens 19To the first refractive surface To the second refractive surface u=u1 n1 v=v2 v1=u2+薄透镜薄透镜20 u=u1 v=v2 n1 v1=u2+n1n2薄透镜薄透镜 Gauss Equation about thin-lens 21Focal length n1=1,in the air n represents the refractive index of the material of thin lens,then the focal lengthSign convention：凸球面对着入射光线，凸球面对着入射光线，r取正号取正号凹球面对着入射光线，凹球面对着入射光线，r取负号取负号薄透镜薄透镜Principal quantity about thin lens22Converging lensDiverging lens r1 0 r2 0 r1 0 f 0薄透镜薄透镜23Dioptric power 表示透镜的折光本领表示透镜的折光本领unit：diopter (屈光度）屈光度）通常所说的眼镜的度数等于屈光度的通常所说的眼镜的度数等于屈光度的1/100倍倍1屈光度屈光度=100度度D越大，系统的折光能力越强越大，系统的折光能力越强薄透镜薄透镜24.单向放大率单向放大率（复习内容）（复习内容）uABAB FOFv又叫长度放大率又叫长度放大率薄透镜薄透镜(lateral magnification)25Example 10-3p191(板书讲板书讲)26 The coaxial system is made up of two or more thin lens。DefinitionsConstructImaging in turn Equation薄透镜薄透镜2.The combination of thin lens 27To the first lensTo the second lens u=u1 v=v2 v1=-u2+薄透镜薄透镜28Example 10-4 (重点重点)(板书讲板书讲)p192293 3、Thick LensThick Lens1）.Concept of thick lens2）.Imaging law30The term thick lens means either a single lens whose thickness is not negligible in comparison with the object distance and the image distance,or any combination of lens such as a corrected camera lens.Thick lens1）.ConceptThin lens31 对每一个单球面，依次应用单球面系统的成像对每一个单球面，依次应用单球面系统的成像规律；规律；利用共轴系统的基点概念利用共轴系统的基点概念把透镜看做是一把透镜看做是一个体系，定义这个系统的三对基点，只要知道这三个体系，定义这个系统的三对基点，只要知道这三对基点的位置，就可以用作图法解决成像问题对基点的位置，就可以用作图法解决成像问题;Thick lens方法一方法一方法二方法二*计算法解决一些成像问题。计算法解决一些成像问题。-Imaging equation方法三方法三2）.Imaging law32a).Two focal point 调整光源在主光轴上的位置，使其光束通过厚透调整光源在主光轴上的位置，使其光束通过厚透镜后变为平行光，这时点光源所在的位置就称为共轴镜后变为平行光，这时点光源所在的位置就称为共轴系统的第一主焦点系统的第一主焦点F1。平行于主光轴的光束，通过系统折射后与主光轴平行于主光轴的光束，通过系统折射后与主光轴相交于一点，称为共轴系统的第二主焦点相交于一点，称为共轴系统的第二主焦点F2。The primary principal focal pointF1The secondary principal focal pointF2Thick lens33b).Two principal points 通过通过F1的入射光线的延长线与出射光线的反的入射光线的延长线与出射光线的反向延长线交于向延长线交于A1点，过点，过A1点所做的垂直于主光轴点所做的垂直于主光轴的平面称为共轴系统的第一主平面，第一主平面的平面称为共轴系统的第一主平面，第一主平面与光轴的交点与光轴的交点H1就称为共轴系统的第一主点就称为共轴系统的第一主点。平行于主光轴的入射光线与其射出线的平行于主光轴的入射光线与其射出线的反向延长线的交点，决定了系统的第二主平反向延长线的交点，决定了系统的第二主平面，第二主点。面，第二主点。F1F2H1A1H2Thick lens34 不管光线在厚透镜中经过怎样曲析的路径，不管光线在厚透镜中经过怎样曲析的路径，在效果上可以看作只在主平面上发生折射。在效果上可以看作只在主平面上发生折射。F1F2H1H2 通过一个主平面上任一点的光线，一定通通过一个主平面上任一点的光线，一定通过另一主平面上的对应点。过另一主平面上的对应点。Thick lens Two principal points 35c).Two nodal points There are another two points N1 and N2,called nodal points which are similar as the optical center of thin lens that rays pass through them without deviated as in next fig.Here QN1 is parallel to QN2.Thick lensN1N2F1F2H1H2QQ 36方法二方法二 厚透镜的基点作图法厚透镜的基点作图法 N1N2F1F2H1H2 通过第一主焦点的光线在第一主平面上折射通过第一主焦点的光线在第一主平面上折射后平行主光轴射出；后平行主光轴射出；平行于主光轴的光线在第二主平面折射后，平行于主光轴的光线在第二主平面折射后，通过第二主焦点；通过第二主焦点；通过第一节点的光线从第二节点平行于入射通过第一节点的光线从第二节点平行于入射方向射出。方向射出。Thick lens371.A ray parallel to the axis is refracted by the second principal plane and passes through the second focal point of a thick lens.2.A ray through the first focal point is refracted by the first principalplane and emerges parallel to the axis.3.A ray through the first nodal point of the thick lens,afterrefraction by the lens,is not deviated and emerges from the second nodal point.38第一焦距第一焦距 f1第二焦距第二焦距 f2物距物距 u像距像距 v都是以主点为基准都是以主点为基准F1F2H1H2 物距、像距和焦距物距、像距和焦距Thick lens 厚透镜的成像公式厚透镜的成像公式 39 v f1 f2 uF1F2H1H2 若系统的最初和最后媒质相同，则若系统的最初和最后媒质相同，则 f1=f2=f，N1与与H1重合，重合，N2与与H2重合，且有成像公式：重合，且有成像公式：Thick lens 厚透镜的成像公式厚透镜的成像公式 40 If the refractive surface of lens is portion of the cylinder,we call the lens is column lens.4.Cylindrical lens41水平光束入射后会聚（发散）水平光束入射后会聚（发散）在竖直方向上在竖直方向上光线不改变方向光线不改变方向点状的物经圆柱透镜折射后成为线状的像点状的物经圆柱透镜折射后成为线状的像Astigmatism425、Lens AberrationsSpherical aberration（球面像差球面像差球差球差）Chromatic aberration（色像差）色像差）431.The essential parts of the eye and accommodation2.Defects of vision and correctionSection 3 The Eye 44角膜角膜(cornea)(cornea)虹膜虹膜(iris)(iris)瞳孔瞳孔(pupil)(pupil)网膜网膜(retina)(retina)黄斑黄斑(yellow spot)(yellow spot)水状液水状液 玻璃状液玻璃状液 眼球剖面图眼球剖面图eye1.The essential parts of the eye and accommodation 45 从光学的观点来看，眼睛是一个由多种介质从光学的观点来看，眼睛是一个由多种介质组成的折射系统。眼内各种不同介质对光线具有组成的折射系统。眼内各种不同介质对光线具有不同的折射作用，进入眼睛的光线，经多次折射不同的折射作用，进入眼睛的光线，经多次折射后，才成像在视网膜上。后，才成像在视网膜上。把眼睛看做是由多种均匀介质组成的共轴把眼睛看做是由多种均匀介质组成的共轴球面折射系统。球面折射系统。根椐古氏（根椐古氏（GullstrandGullstrand）的计算，这一系统的计算，这一系统的光学性质大概有书中表的光学性质大概有书中表11-211-2所给的平均数值。所给的平均数值。1).古氏平均眼古氏平均眼眼睛眼睛 a.Optic characters of the eye 46 角膜与空气的折射率相差最大，且角膜的曲率角膜与空气的折射率相差最大，且角膜的曲率半径最小（约为半径最小（约为5mm），），因此，角膜的折射本领最因此，角膜的折射本领最大，它对进入眼中的光线起主要的折射作用。大，它对进入眼中的光线起主要的折射作用。2).简约眼简约眼(reduced eye)生理学生理学上常常把眼上常常把眼睛简化为睛简化为单单球面折射系球面折射系统统，叫做，叫做简简约眼约眼(reduced eye)。n=1.33f2=20mmF2F1f1=15mm r=5mmCeye a.Optic characters of the eye 473).眼睛的调节眼睛的调节(accommodation)眼睛之所以能眼睛之所以能够看清远近不同的够看清远近不同的物体，是由于眼的物体，是由于眼的焦度可以在一定范焦度可以在一定范围内改变围内改变Far point：正常人在无穷远正常人在无穷远Near point：正常人在正常人在1012cmDistance of distinct vision:正常人为正常人为25cmeye调节调节调节调节(accommodation)(accommodation)(accommodation)(accommodation)眼睛改变焦度的过程叫调节眼睛改变焦度的过程叫调节.48Visual acuity：The eyes can distinguish the least visual angle 从物体两端射从物体两端射到眼中节点的光线到眼中节点的光线所夹的角度所夹的角度0.1 0.2 0.3 1.0 1.2 1.510 5 3.3 1.0 0.8 0.67 eyeb.Visual angle：49502).Myopic eye 1).Normal eye 3).Hyperopic eyeeye2.Vision Defects of vision and correction 512)Myopia eyeThe function of lens is to form a virtual image on the far point of the myopia eye.Example11-5523)Hyperopic eye远视眼远视眼The function of lens is to move the objectfarther away from the eye to a point where a sharp retinal image can be formed.远视眼的矫正远视眼的矫正近点近点10-12cm距距离离534)Astigmatism eye 角膜表面的曲率半径不一致，不是球面，光角膜表面的曲率半径不一致，不是球面，光线经过眼球的不同经线后就不可能会聚于同一焦线经过眼球的不同经线后就不可能会聚于同一焦点，在网膜上不能形成清晰的像。点，在网膜上不能形成清晰的像。矫正方法是配适当的圆柱透镜。矫正方法是配适当的圆柱透镜。老花眼不属于屈光不正，是随着晶状体调老花眼不属于屈光不正，是随着晶状体调节机能减退出现的近点远移的现象，补救的办节机能减退出现的近点远移的现象，补救的办法是在看近物时戴适当的凸透镜。法是在看近物时戴适当的凸透镜。eye54Eg1:The near point of a certain eye is 100 cm in front of the eye.what lens should be used to see clearly an object at the normal reading distance?v=100cm=1m Solution:55Eg.2 Eg.2 The The far far point point of of a a myopia myopia eye eye is is 0.4m 0.4m in in front front of of the the eye eye，what what lens lens should should be be used used to to see clearly the object at infinity?see clearly the object at infinity?v=0.4m Solution:56.MagnifierSection 4 Magnifier Section 4 Magnifier 57Magnifier1)The apparent size of an object is determined by the size of its retinal image.which,in turn,if the eye is unaided,depends upon the angle subtended by the object at the eye.2)When one wishes to examine a small object in detail,one brings it close to the eye in order that the angle subtended and the retinal image may be as large as possible.58Magnifier 25cmmagnifier3)Since the eye cannot focus sharply on objects closer than the near point.by placing a converging lens in front of the eye,the accommodation may,in effect,be increased.The object may then be brought closer to the eye than the near point and will subtend a correspondingly larger angle.A lens used for this purpose is called a magnifier.The lens forms a virtual image of the object.59.Magnifier 25cmfyymagnifier角放大率角放大率:The angular magnificationAt normal reading distance(f in cm)60 In order to see clearly a small object that can not be seen clearly using ones unaided eye.When an angular magnification higher than that attainable with a simple magnifier is desired,it is necessary to use a compound microscope,usually called merely a microscope.Section 5 MicroscopeSection 5 Microscope61.The essential elements of microscopeSection 5 MicroscopeSection 5 Microscope.Overall magnification of the microscope .The resolving power of microscope.A few special biological and medical microscopes62ocular L2Objective L1F1F2microscope.The essential elements of microscope63.The overall magnification of microscope yy1F1F2y2L1L2The lateral magnification m of objectiveThe angular magnification Of ocular 25cmf2microscope6465.The resolving power of microscope66.The resolving power of microscope67显微镜的分辨本领显微镜的分辨本领The resolving power of microscope68The least distinguished distance of optics system.The resolving power of microscope物镜的数值孔径物镜的数值孔径 methods of increasing The resolving power of microscope紫外显微镜紫外显微镜荧光显微镜荧光显微镜电子显微镜电子显微镜Increasing the numerical apertureThe space between the object And the objective is filled with an oilThe resolving power 1/z decided only by the objectivemicroscopeDecreasing the light wavelength6970711.偏光显微镜（偏光显微镜（polarizing microscopes)以可见光的偏振特性对具有双折射现象和旋光性以可见光的偏振特性对具有双折射现象和旋光性的的物质进行研究鉴定的必备设备。物质进行研究鉴定的必备设备。4 10 25 40 5 10 16 2.电子显微镜电子显微镜(electronic microscopes)用波长很短的电子射线代替可见光做成的。用波长很短的电子射线代替可见光做成的。(80-100万倍）（万倍）（0.144纳米）纳米）microscope.A few special biological and medical microscopes724.荧光显微镜荧光显微镜 有些物质（维生素有些物质（维生素A、核黄素、硫胺素等）受核黄素、硫胺素等）受紫外线照射能发出荧光，还有些物质（细菌）可以紫外线照射能发出荧光，还有些物质（细菌）可以用荧光染料给其染色。用荧光染料给其染色。灵敏度高灵敏度高用紫外线作光源，但观察的是荧光。用紫外线作光源，但观察的是荧光。3.紫外显微镜紫外显微镜波长短，分辨本领强；波长短，分辨本领强；生物原生质对可见光几乎是完全透明的，但对生物原生质对可见光几乎是完全透明的，但对紫外线的吸收却不同，可用以观察单细胞组成物。紫外线的吸收却不同，可用以观察单细胞组成物。microscope.A few special biological and medical microscopesHome work:，:11-7,11-8，11-9,11-10,11-11,11-12,11-14,11-1573