应用光学(第四章)2.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,Chapter 4 Plane surfaces and Prisms,The behavior of a beam of light upon refraction or refraction is of basic importance in geometrical optics,Plane surfaces,often occur,in nature,Artificial plane surfaces,are used in optical instruments,to bring about deviations or lateral displacements of rays,as well as,to break light into its colors,.The most important devices of this type are,prisms,.,2.1 Parallel beam,Parallel beam,remains,parallel,after reflection or refraction,at a plane surface.,Refraction causes a change in width of the beam which is easily seen to be in the ratio ,whereas the reflected beam remains of the same width.,There is also chromatic dispersion of the refracted beam but not of the reflected one.,(a)external reflection,(c)Total reflection at or great than the critical angle,(b)Internal reflection at an angle smaller than the critical angle,Reflection at a surface where,n,increases,is called,external reflection,.It is also,frequently termed rare-to-dense reflection,because the relative magnitudes of,n,correspond roughly(though not exactly)to those of the actual densities of materials.,Fig.2(b)shows a case of,internal reflection,or,dense-to-rare reflection,.In this particular case the refracted beam is narrow because is closed to 90,External reflection and internal reflection,2.2 The critical angle and total reflection,no refracted light,Critical,angle,Refraction and total reflection,The critical angle is the limiting angle of refraction,total reflection beyond the critical angle,A formula for calculating the critical angles is obtained by substituting ,or in Snells law,In the limiting case,where,the incident rays approach an angle of 90with the normal,the refracted rays approach a fixed angle beyond,which no reflected light is possible,.This particular angle ,for which ,is called the,critical angle,.,So that,Always less than unity,接近，逼近,The critical angle for the boundary separating two optical,media,is defined as,the smallest angle of incident,in the medium of greater index,for which light is,totally reflected,.,Totally reflection is,really total in the sense,that,no energy is lost upon reflection,Total reflection prisms,Total reflection,Porro,Dove or intverting,Amici or roof,Triple mirror,Lummer-brodhun,Reflecting prisms utilizing the principle of total reflection,The angles of incidence can be,as small as 45.,The requirement sets,a lower limit,on the value of the index,n,of prism.,Index of air,Low refractive indices of optical materials,Lucite(,n=1.49,)Fused quartz(,n=1.46,),一种有机玻璃材料，树脂,熔石英,Refractometers,（折射计）,Instruments for,the determination,of,refractive index,Refraction by the prism in a Pulfrich refractometer,2.3 Plane-parallel plate,Refraction by a plane parallel plate,It emerges,parallel,to its,original direction,but,with a lateral displacement,d,which,increases with the angle of incidence,出射,The displacement d,Starting with the right triangle ABE,we can write,By the,trigonometric relation,for,the sine of the difference between two angles,直角三角形,位移,三角法的,From,Snells law,we obtain,Therefore,From 0up to appreciably large angles,d is nearly proportional to,2.4 Refraction by a prism,The deviation produced by the first surface is not annulled by the second,but is further increased,.,The,chromatic dispersion,is also increased,and,this is usually the main function of a prism.,The reflection at the second surface,as well as at the first surface,The total angle of deviation,As,or,2.5 Minimum deviation,If the prism is,rotated continuously,in one direction above an axis,parallel to the refracting edge,the angle of deviation,will be observed to,decrease,reach a,minimum,and then,increase,again.,The smallest deviation angle,called,the angle of minimum deviation,occurs at an particular angle of incidence where the refracted ray inside the prism makes,equal angles with the two prism faces.,How to prove the angles be equal?,The measurements of the refractive index,In the triangle ABC,;For the triangle ABN,Consequently,Since by Snells law,Place the sample,in the form of a prism,on the table of a spectrometer and measuring the angles and .,The former for each color desired.,When prisms are used in,spectroscopes,(,分光镜,）,and,spectrographs,（,摄谱仪,）,they are always,set as nearly as possible at minimum deviation,.,2.6 Thin prisms,When the refracting angle becomes small enough to ensure that,Thin prism in air,The power of a prism,It is customary to measure,the power of a prism,by,the deflection of the ray in centimeters at a distance of 1m,in which case,the unit of power,is called,the prism diopter(D),棱镜折光度,棱镜的折光本领,the power of the prism in diopter,e.g.,For the dense flint glass,.The refracting angle of,1-D,prism,should be,2.7 Combinations of thin prisms,The Risley or Herschel prism,a combination of,two thin prisms,of,equal power,which can be,rotated in opposite dirctions in their plane,.,The device is equivalent to,a single prism of variable power,When the prisms are,parallel,the power is,twice that of either one;,When they are,opposed,the power is,zero,.,The resultant deviation,Since almost always,and,2.8 Reflection of divergent rays,When,a divergent pencil of light,is reflected at a plane surface,it,remain divergent,.,Object distance=image distance,The point Q is said to be a,virtual image,of Q,Real image,2.11 Refraction of divergent rays,Virtual image,The image appears,closer to the surface,As the observer changes his position,the virtual image,moves,closer to the surface,and,along the curve formed by the successive image,Note that far away these images are for larger angles of and .,Image position of an object in air as seen by an observer under water;,Virtual image,2.12 Images formed by paraxial rays,Rays for which,angles are small enough,to permit setting,the cosines equal to unity,and,the sines and tangents equal to the angles,are called,paraxial rays,Paraxial rays for an object in water and observed from the air above.,Angles and are very small,In triangles QAB and QAB,Applying Snells law,For angles and are very small,so,Paraxial rays,The ratio of the image to object distance for paraxial rays is just,equal to,the ratio of the indices of refraction,2.13 Fiber optics,When light,in an optically dense medium,approaches,the boundary of a less dense medium,at angle ,greater than the critical angle,it will,totally reflected.,Light from a flashlight follows a bent transparent rod,by total reflection,All attenuation of an incident beam is attributable to,reflection from two end and absorption by the fiber material,An ordered array of fine glass,fibers,can be used to,transmit images,from one end A to the other A,along any cured path.,The method for producing coated fibers,Insert a thick,high-refractive-index glass,rod in,tubing of,lower index,.,The individual fibers,are about,2um in diameter,.This is about,two wavelengths of visible light,.Such bundles can resolve,approximately 250 lines per millimeter.,Two wavelengths of light,is an,approximate limit,for,image transmission.,Applications of fiber optics,One of the most important is,in the field of medicine,.,Cystoscope,or catheter-type instrument.,膀胱镜,导管,n,2,Refraction by plane interface&Total internal reflection,n,1,n,1,n,2,C,P,1,1,1,1,2,2,Snells law n,1,sin,1,=n,2,sin,2,Light propagated in an optical fiber,The numerical aperture of an optical fiber,