1、Chapter spherical systemythin lenses and thick lenses球面系統(tǒng)厚透鏡與薄透鏡3.1 Focal point and focal length 焦點(diǎn)與焦距3.2 Lens formula for thin lens 薄透鏡公式 3.3 Thick lens 厚透鏡3.4 Spherical mirror 球面反射鏡Several standard forms of lens Positive: thicker at the center Equi-convex plane-convex positive meniscus Negative: t

2、hinner at the center Equi-concave plane-concave negative meniscus 3.1 Focal point and focal length real focusDiverging rays from F are refracted into a beam parallel to axis.virtual focusConverging rays toward F.Parallel incident beam is refracted, converge into F. Diverge as if it come from FFocal

3、point and focal lengthF: primary focal point f: primary focal lengthF: secondary focal point f: secondary focal length 1、 Image formation real image and virtual image Graphical constructionSharply real image can be formed on the screen. Virtual image can be seen by human, but it can not be recorded

4、.Because refracted rays do not come from, only appear to do so.2、 Conjugate points and planes Principle of the reversibility of light rays ifwere an object , an image would be formed at .The object and image are interchangeable or conjugate ( ): are called conjugate points.The plane through these po

5、ints perpendicular to the axis are called conjugate plane .3、 Calculation methodfrom 2.1 : Gaussian formula for a single spherical surface : object (image )distance If or 4、Graphical constructions The parallel ray method The rays from object point B traveling parallel to optical axis will be refract

6、ed to pass through F. The rays BC pass through the center of curvature is un-deviated, because it is in line and C is nodal point. The two rays are sufficient to locate the tip of the image at B. The rays which pass through F will be refracted parallel to the optical axis.5、Oblique-ray methodsMethod

7、s 1: AM: represent any ray incident on the surface. Through the center of C,A dashed line is draw, parallel to AM,Crosses the secondary focal plane at N, The line MN is refracted ray, it crosses the axis of A.Methods 2:From similar triangles (p53)6、Magnification of spherical surface Lateral magnific

8、ation: the ratio between transverse dimension of the final image and the corresponding dimension of the original object. if is positive ,image is erect and virtual if is negative ,image is inverted (inverse )and real .7、Reduced convergenceReciprocals , , , , Actually represent curvature, , . are rad

9、ii , V , V are called reduced convergence .Because they are direct measures of of wavefronts .: define the refracting power . All distances are measured in meters ,the reduced V, V, P are in units called diopter .Definition: whose thickness is considered small in comparison with the distances such a

10、s,.3.2 Lens formula for thin lens 1、 Focal point F F(just like surface ) Primary focal point F is an axial point that any ray coming from it or proceeding toward it travels parallel to the axis after refraction. Secondary focal point F: that any incident ray traveling parallel to the axis will proce

11、ed toward (or appear to come from) F after refraction. For lens with the same medium on both sides, we have 2、 Derivation of the lens formula image formula: (1) (2)(1)-(2) yield the desired formula Gaussian form Newtonian form Lateral magnification:From picture: Newton (1)(2): Gauss Optical power :L

12、ens Makers formula :If a lens is to ground to some specific f ,the radii of curvature must be so chosen to satisfy the equation.3、 Thin lens combination First apply the graphical method to find the image distance, then shown how to calculate it by lens formula. Graphical method: Calculation method:F

13、or lens 2: Apply 4、 Derivation of lens makers formula (1) (2)For thin lens Add (1)+(2) for for in water for in air Thin lens in contact Parallel rays are refracted by first lens toward its secondary, second lens brings the rays together at ,for second lens is the object distance ,is image distance.F

14、or lens 2 The power of combination is equal to the sum of the power of individual lens.3.3 Thick lens1、Conjugate relation for thick lens Relation between object and image Gaussian lens formula: When Power formulas Thick lens : If d=0(thin lens),Conclusion: With lens combination as a think lens, the

15、position of the cardinal points of a combination of two thin lenses in air can be calculated by means of the thick lens formulas. Thick lens The formula can be used in double separated lens if take.2、Special thick lensesa positive lens with equal radii of curvaturea negative lens with concentric sur

16、faceA lens with equal radii surrounded by a medium of lower index has a small but positive power. The spacing HH is equal to the lens thickness d.Concentric lens (both surfaces have the same center of curvature), if , the lens has a negative power with long focal length.HH=d located some distance fr

17、om and to the right the lens.HH=0 principal point coincide with the common center.3.4 Spherical mirrorThe image from a spherical mirror is in some respects superior to that from a lens, not only in the absence of chromatic effects, but their applications are not so broad as those of lenses because t

18、hey do not offer the same possibility for correction of other aberration.1、Focal point and focal length concave mirrorconvex mirror(virtual focus)Concave mirror: all rays are brought to a common focus at F, F is called the focal point, distance AF is called focal length.Convex mirror: refracted rays

19、 diverge as though they come from common point F. Mirror has only one focus FTriangle TCF is isosceles ,Gauss optics , one-half the radius 2、Graphical constructions A: parallel rays incident on a concave mirror but inclined to the axisB: auxiliary axis diverged rays incident on a concave mirror in Fig.B, when the object AB is moved toward the center of curvature C, the image also approaches C and increases the size.When it reache