1、Review:,1. Chart Illustration For Image Formation(7),2. Image Position And Size,Gaussian equation,Newtonian equation,2.10 Magnification Of Optical Systems,F,F,H,H,B,B,A,A,-x,-f,-l,-y,f,l,Object plane,Image plane,X,y,U2,U1,-U2,-U1,Fig. 2.32,Lateral ( or transverse) magnification 垂軸放大率 Longitudinal ma

2、gnification 軸向放大率 Angular magnification 角放大率,Magnification Of Optical Systems,2.10.1 Lateral ( or transverse) magnification,According to Newtonian equation and Gaussian equation we can have,2.10.2 Longitudinal magnification,Suppose the object plane of an optical system move a small distance dx along

3、 the system axis, the image plane of the system will also move a small distance dx along the axis.,(1) Gaussian equation,Differentiating (微分) on both sides of the above equation and according to the Fig. 2.32, we have,(2) Newtonian equation,Differentiating (微分) on both sides of the above equation, w

4、e have,(3) Angular magnification,In paraxial region,In fig.2.32,Gaussian equation:,Newtonian equation:,(4) Relationship among the three magnification,2.11 Optical ( Lagrange )Invariant (物像空間不變式),In paraxial region:,Optical ( Lagrange )Invariant,The optical invariant for ideal optical systems:,If the

5、 indices of object and image space are equal , we have,For a reflected surface,odd number reflection,even number reflection,2.12 relationship between f and f,If the indices of object and image space are equal , we have,位于空氣中的光學(xué)系統(tǒng)，其像方焦距和物方焦距大小相等，符合相反(EFF),2.12.1 Image Position (n=n,f=-f),According Ne

6、wtonian Equation ,we have,According Gaussian Equation, we have,2.12.2 Magnification (n=n,f=-f),Lateral ( or transverse) magnification Longitudinal magnification Angular magnification,2.12.3 Relationship among the three magnification,According to Equ.(2.33) , we have,The couple of planes whose angula

7、r magnification is equal to 1 are called nodal planes. The plane in the object space is called the first nodal plane and the plane in the image space is called the second nodal plane.,2.13 Nodal Planes And Nodal Points (節(jié)平面和節(jié)點),The intersection points of the two nodal planes and the axis are called

8、the first nodal point and the second nodal point separately, denoted by J and J.,Properties:,Any incident light ray which passes through the first nodal point J, after passing through the system, will pass through the second nodal point J and parallel to its original direction, as shown in Fig.2.35.

9、,According to Equ. (2.32), we have,?,?,When an optical system is bounded on both sides by air(n=n), we have,On this condition, J coincides with H and J coincides will H, that is to say, the nodal points coincide with the principal points, as shown in fig.2.36.,(7) Any incident rays which pass throug

10、h the first principal point will emit from the second principal point and parallel to the incident ray.,The seventh Conclusion of Chart illustration：,The first application of the property of nodal points: to find the image of the object,H,H,J,J,F (A1),1,2,The second application: to measure the other

11、 nodal point of an optical system,?,H,H,J,J,A1,F,A2,If the rotating axis passed through the second nodal point J, the image point will not shift,A,B,B1,A1,A,A1,B1,B,J,J,Object lens,The third application: to use panoramic camera (全景、周視)照相,Object,Image,Homework,P62, 1-8, 12-15,2.14 Image Height Of The

12、 Object At Infinity,We use the field angle (視場角)to denote the object position which is at infinity. : start from the axis to the ray. It is positive if the angle rotates right-handed and negative if left-handed.,-,-f,f,H,H,I,I,F,F,y,Fig. 2.39 Image height of infinity object,From fig.2.39 we know,(2.

13、46),If the system is bounded on both sides by air, then f=-f, we get,-f,f ,H,H,I,I,F,F,y,Fig. 2.40 Object height and its infinity image,2.15 The Combination Of Ideal Optical Systems,f, f,F, F,H, H ?,2.15.1 position of focal points(two lens),F1,H1,H1,F1,F2,- f 1,d,2,f 1,- f 2,H2,H2,F2,f 2,D,Suppose t

14、he focal lengths of two known sub-systems are f and f the distance between the second focal point F1 of the first system and the first focal point F2 of the second system is denoted by.,The sign convention of ,: starts from F1 to F2 , positive if it goes from left to right. According to the properti

15、es of the focal points, any parallel incident ray will cross point F1 after passing through the first system, and the intersection point of the emerging ray and the axis after passing through the second system is the second focal point F of the combined system.,H,A1,F,u,F1,A1,H1,H1,F1,F2,- f 1,1,2,d

16、,2,2,f 1,A2,H,- f 2,H2,H2,F2,F,-u,f 2,f,- f ,-xF,- xH,-lF,-lH,xF,xH,lF,lH,A2,Object,Image,D,Fig. 2.41 The combination of two ideal systems,1,2,xF: start from F1 to F,xH: start from F1 to H,xF: start from F2 to F,xH：start from F2 to H,lF：start from H2 to F,lH: start from H2 to H,lF：start from H1 to F

17、,lH: start from H1 to H,positive if they go from left to right.,A1,F1,H1,H1,F1,F2,A2,- f 2,H2,H2,F2,F,f 2,xF,D,Object,Image,F1 and F are two conjugate points, by applying Newtonian equation we have,(2.49),F,u,F1,H1,H1,F1,F2,- f 1,1,2,2,f 1,H2,H2,F2,-xF,Object,Image,D,F and F2 are two conjugate point

18、s, by applying Newtonian equation we have,(2.50),2.15.2 Equations of focal lengths,A1,F1,H1,H1,F1,F2,A2,- f 2,H2,H2,F2,F,f 2,D,Object,Image,H,I1,I1,I2,I2,- f ,xF,A2HF I2H2F， I2H2F1 I1H1F1,A2H I1H1 ；I2H2 I2H2,f 1,(2-51),n1，n2，n3,(2-52),n1=n2=n3=1,Is called Power光焦度或屈光度,d0, is an important concept and

19、 not too big commonly. Its unit is m-1, denoted by D.,Examples,（1）0, (f 0) ,會聚光組，愈大（焦距越 短），匯聚本領(lǐng)愈大，反之亦然。 （2）0, (f 0)，發(fā)散光組，絕對值愈大， 發(fā)散本領(lǐng)愈大，反之亦然。 （3）平行平板，f 為， ，對光束不 起會聚或發(fā)散作用。,Conclusions,2.16 Ray tracing for ideal optical systems,(2-61),(2-62),2.17 Equation For Calculating Positions Of Principal Planes A

20、nd Focal Points Of A Single Lens,A single lens can be taken as an optical system.,H1,H1,H,H,H2,H2,F1,F1,F2,F2,F,F,d,-f1,f1,-f2,f2,lH,-lH,-f,f ,-xF,xF,Fig. 2.45 Cardinal planes and points of a single lens,-lF,lF,n,1,1,(2.16),(2.17),n1=n3=1, n2=n,(2-63),d,lH=xF+f1-f ； lH =xF +f2 -f,From Fig. 2.45 we can have,From Fig. 2.45 we can have,For a thin lens we can have,-lF=-f-lH ； lF=f +lH,From Fig. 2.45 we can have,Exam