ch2-2 thin lens.ppt

1、3 Thin Lens （薄透镜）,A transparent homogeneous medium bounded by two spherical surfaces is referred to as a spherical lens. If the thickness of such a lens (shown as d in Fig.2-3-1 below) is very shorter than that of object and image distances, and also than radii of curvature of the surfaces, the lens

2、 is referred to as a thin spherical lens. Different types of lenses are shown in Fig.2-3-2. The line joining the centers of curvature of the spherical refracting surfaces is refracted to as the axis of the lens. These interfaces are most frequently spherical segments and are often coated with thin d

3、ielectric films to control their transmission properties. A1 is very close to A2, and both of them can be regarded as one point, this point is defined as the optical center O.,Q,d,A1,A2,C,Fig.2-3-1,Q1,Q,3.1 thin-lens equations,Return to the discussion of refraction at a single spherical interface, L

4、ets locate the conjugate points for a lens of index nL surrounded by a medium of index n1 where the location of the conjugate points S and Sis given by,（3-1）write on black board,so（3-2）become as：,（3-3）,（3-1）（3-3）we get：,If we drop the subscripts of S1 and S2 in the equation (3-4), let S denotes obje

5、ct distance and S denotes image distance, (3-4) is rewritten as,If the lens is thin enough,（35）,s,h,Accordingly , we have the very useful Thin-Lens Equation, This equation often referred to as the lens makers Formula,from（31）,If s is moved away to infinity, the image distance s becomes the focal len

6、gth f .,（3-6）,By using（32），（35）can be rewritten as：,（3-8）,Which is the famous Gaussian Lens Formula 高斯公式。,for thin lens,（3-7）,The lens which has real focal point（f and f 0）is referred to positive lens(正透镜)，we know from (3-6) that this kind lens requires 1/r1 1/r1 due to 1 . The lens which has virtue

7、 focal point（f and f 0） is referred to negative lens, this kind lens requires 1/r1 1/r1 due to 1.,Converging lens,Diverging lens,C2,C1,A,B,O,O is the optical center (光心) of the lens. Rays passing through O may, accordingly, be drawn as straight lines due to no refraction. Generally, several bundles

8、of rays passing though lens in a narrow cone will be focused on a spherical segment surface . Since the ray cone must indeed be narrow, can satisfactorily be represented as plane normal to the symmetry axis and passing though the image focus. It is known as a focal plane(焦平面).,f,Focal plane,Fi,Fo,In

9、 water,here n is the index of glass relative to water。,Example: The index of one convex lens nL=1.52, its focal distance f is 40cm, while it is put in water (n=1.33), calculate the focal distance.,solution : in the air,so,results：,3.2 Newton equation of thin lens, Transverse magnification,There are

10、two methods for the image calculation according to two different coordinate (坐标)systems: Gaussian equation Newtonian equation,the reference point of Gaussian Lens Formula is the optical center C. The position of object and image also is with reference to focal points, sign conventions for x and x is

11、 shown as follow:,(2) Image point Q lies on L-side of focal point F, ; image point Q lies on R-side of focal point F, .,x,f,F,Q,O,s,Q,O,F,-f,x,s,(1) Object point Q lies on L-side of focal point F, ; Object point Q lies on R-side of focal point F, .,We can get relations from Fig. ：,Substitute s (s) i

12、n Gaussian Formula with x+f(x+f),This is Newton equation （for thin lens， ）,we get the result ：,(3-16),x,f,F,Q,O,s,Transverse magnification ：,For both of spherical interface, we have the transverse magnification respectively：,For thin lens, we have the relations,So we get the result：,While index of o

13、bject and image space is the same，,This is the transverse magnification of the thin lens,h,s,(3-19),Longitudinal magnification:,Suppose the object plane of an optical system move a small distance dx along the system axis, the image plane of the system will also move a small distance dx along the axi

14、s.,(1)Gaussian equation,Differentiating (微分)on both sides of the above equation, we have,(2) Newtonian equation,Differentiating (微分)on both sides of the above equation, we have,3.3 lens group,Generally, lens group is the optical system which consist of two or more than two lenses.,If the lens group

15、is made up of two lenses , for the first one, we have,For the second one,so,Plus the two formula above ：,Here s is object distance, s is image distance.,The focal distance f,The reciprocal(倒数) of focal distance f is called focal power（光焦度）. so,The focal power of lens group is the summation of the fo

16、cal power of lenses,When length unit is meter, optical power is diopter(屈光度), (sign D）. Notes: The degree of glass what we usually use is 100 times of the diopter, for example, concave lens, f=50.0cm, focal power P=1/(-0.50m)=-2.00，the degree is 200.,3.4 Illustration of Imaging,3.4 focal plane 焦平面,I

17、n this section we use illustration method to locate the image. For an ideal optical system all of the rays emitted from one object point will converge at one image point, so before we locate the image point we need only locate two special emitted rays.,Plane normal to the symmetry axis passing thoug

18、h focal point F in object spacefocal plane in object space (物方焦平面),Plane normal to the symmetry axis passing though focal point F in image spacefocal plane in image space(像方焦平面),3.5 light path diagram,To determine the conjugate image, three light rays can be draw through top point on object.,(1) Ray

19、s being parallel to the optical axis，after travelling through lens, propagate through focal point in image region.,(2) Rays going through the optical center (lens center) keep the same direction .,(3) Rays going through focal point in object region, after travelling through lens, are parallel to the

20、 optical axis.,focal plane,P,optical axis,secondary optical axis,Symmetrical axis of lens is optical axis OP secondary optical axis,Optical path diagrams below are some examples to determine the position of image.,(a) Object is located outside the scope of focal length of convergent lens;,(b)Object

21、is located inside the scope of the focal length of convergent lens;,(c)Object is located outside the scope of focal length of divergent lens,F,F,F,Drawing method to determine conjugate rays: The conjugate rays of any incident ray or image of object point on axis can be determined by using the nature

22、 of focal plane,Q,M,O,Q,O,M,3.6 lens group imaging,method（1）by using imaging formula （2）by using drawing method,例1,的照相机已经对远处的景物调好了焦面，现在拟对在镜头前 处的人拍照。,求：在像面不改变位置的条件下，镜头应移动多少？,解：,Q,2000mm,无限远物必定成像于焦平面,设对 处的人，镜头需向前移动 方能在原焦平面位置成清晰的像.,整理得：,即照相镜头需向物方运动5.26mm。,例2,凸透镜和凹透镜的焦距分别为20.0cm和40.0cm， L2在L1之右40.cm，旁轴小

23、物放在L1之左30.0cm，求它的像。,作图法：,计算法：,第一次成像,代入数值，求得,横向放大率,第二次成像,横向放大率,倒立,正立,倒立,例3,Where is the final image?,Solution,First we locate the image position for the first lens while neglecting the second lens:,We see that the image of the first lens locate 10cm on the right of the second lens .We apply the thin

24、lens equation to the second lens with,The final image lies (20/3)cm on the right of the second lens.,The magnification of each lens is given separately by,Hence ,the final image is inverted and enlarged.,4 perfect optical system（理想光具组）,4.1 perfect imaging formation and colinear transformation(共线变换),

25、Every concentric beam still keep concentric after being transformed by the optical system from object side to image side. This optical system is called perfect optical system. In fact, there is no perfect optical system, imaging in the paraxial region of a coaxial(共轴的)spherical system can be regarde

26、d as perfect imaging. The concept of perfect optical system is obtained by abstracting and idealization base on the model.,Properties of perfect optical system： Each point A in object space corresponds one point B in image space (conjugate point) 2. Each line in object space corresponds one line in

27、image space (conjugate line) 3. Each plane in space corresponds one plane in image space (conjugate plane),These relations are called colinear transformation(共线变换) . Studying the properties and law of the transformation has the guiding significant for us to study the optical system. If the optical s

28、ystem is axial symmetry, it also has the properties except three properties above as follow:,Conjugate point of any point on the optical axial is still on the optical axial. Conjugate plane of any plane normal to optical axial is perpendicular to optical axial. The transverse magnification keep cons

29、tant in the same plane normal to optical axial . The transverse magnification keep unequal in the different plane normal to optical axial. If there are two plane on which the magnification is equal, the magnification on any plane is equal. In the optical system, the light beams parallel the optical

30、axis will be kept.,4.2 cardinal point (基点) and cardinal plane (基面) of coaxial complete optical system,When the position of optical center O and focal length (f, f) are presented, we know in the section of thin lens that the relations between the object and image is confirmed, neglecting the other de

31、tails, such as index nL , radii of curvature etc. As the same, for the coaxial optical system, no matter how its construction is complex, the conjugate relations between object and image can be confirmed by several points while the optical system is regarded as perfect one. These several point are c

32、ardinal point (基点)and cardinal plane(基面)of complete optical system,The image point, which is formed by the light rays from the axial object point in infinite, is called the second focal point(像方焦点), F, as shown in Fig. below. And the object point, which is correspond to image point in infinite, is c

33、alled the first focal point(像方焦点), F.,H,F,（1） focus and focal plane,The second focal point and the axial object point in infinite are a couple of conjugate points.,The plane, which crosses the second focal point and is vertical to (= perpendicular to) the axis, is called the second focal plane(像方焦平面

34、).,But the telescope system has no focal point and focal plane,That means, there must be a conjugate image planes whose magnification equals to 1. These two object and image planes are called principal planes, in which the object plane is called the first principal plane and the image plane is calle

35、d the second principal plane.,According to Eq. above ,different conjugate object and image planes correspond to different magnifications.,principal planes,(2) principal point（主点) and principal plane (主平面),The intersection points of the two principal planes and the axis are the principal points(主点),

36、also, the point in object space is called the first principal point and in image space the second principal point, which are denoted by capital letter H and H respectively.。,Note：the principal plane is not always between the two interfaces of lens. Sign convention for object (image) distance and foc

37、al distance： In object space: Q( or F) lies on L-side of H, s（or f)0， Q (or F) lies on R-side of H，s（or f)0.,4.3 relation between object and image,We can get the image by illustration or calculation.,和,We have the relation from Fig. above,Gaussian equation,Angular magnification,Newtonian equation,la

38、teral magnification,Here u and u is the angle between the conjugate light rays and the optical axis .,We can get the result from the figure.,The lateral magnification is in inverse proportion to the angular magnification,For a single refraction interface,This is H.von Helmholtz（亥姆霍兹)equation, in paraxial region tguu , the equation become to Lagrange-Helmholtz equation.,nodal point（节点）,To discuss the relation of conjugate line, it is necessary to introduce the concept of nodal poi