Chapter 36Spherical mirror formulasThe lens maker’s formula (lens in vacuum or air)Slide 4More examplesSteps to determine the signsThe lens maker’s formula (lens in a medium)Slide 8More examplesOne more exampleDetermining Signs for Thin LensesSign Conventions for Thin Lenses, summary table. Please compare it with the mirror case.Example 1More exampleAnother example (?) What is the equivalent focal length of two lenses in ContactCombination of Thin Lenses, example: final the final image.Optical instrument: magnifier. Size of an object or an imageAnother magnifier: the compound MicroscopeHow a compound microscope worksMagnifications of the Compound MicroscopeAnother optical instrument: the telescopesHow a refracting telescope worksHow a reflecting telescope worksChapter 36Image Formation 21. Thin Lens2. Multi lens/mirror systemSpherical mirror formulas1 1 1p q f+ =IOhqMh p� =-Object distance, image distance and focal length:Focal length and sphere radius:2Rf =Object distance, image distance and magnification:2Rf =-Converging mirrorDiverging mirrorThe lens maker’s formula (lens in vacuum or air)211111RR)n(fn : index of refraction of the lens material.R1 : radius of near surface. R2 : radius of far surface. The sign conventions for the radii of the two surfaces:1. The near or far surface of the lens is with respect to the focal point F. Near side is surface 1, far side is surface 2. 2. The sign of the radius is then defined as:“+” if the center is on the far side; “-” if the center is on the near side 1. In this convention, positive f means converging lens, negative f means diverging lens.Fnear surfacefar surfaceMore examplesSteps to determine the signsPick up the focal point, hence the focal length in question.Mark the near surface S1, and far surface S2.Based on the curve of these two surfaces, mark the center C1 for S1 and C2 for S2.Mark R1 for S1 and R2 for S2.Now decide on the sign of R1 and R2, based on its center on far side (+) or near side (-).211111RR)nn(fmediumlensFnear surfacefar surfacenmediumThe lens maker’s formula (lens in a medium)Example: prove for a thin lens, the focal length on both side of the lens is the same.Fnear surfacefar surfacenmedium211111RR)nn(fmediumlensMore examplesA thin lens has a focal lens of fa = 5 mm in air. The index of refraction of the lens material is 1.53. If this lens is placed in water (n = 1.33), what will the lens’ focal length in water?One more exampleA thin lens has a near surface with a radius of curvature of −5.00 cm and a far surface with a radius of curvature of +7.00 cm. (a) Is the lens converging or diverging? (b) What is the focal length of the lens if the index of refraction of the material is 1.74?Determining Signs for Thin LensesThe front side of the thin lens is the side of the incident light The light is refracted into the back side of the lens. So a real image is formed on the back side of the lens while a virtual image is formed on the front side of the lens.Real object sideVirtual object sideReal image sideVirtual image sideLens locationSign Conventions for Thin Lenses, summary table. Please compare it with the mirror case.1M < 1M =1M >Image smallerImage same size Image largerExample 1Find the image distance./mdi = 1.0 mMore exampleA small light bulb is placed a distance d from a screen. You have a converging lens with a focal length of f. There are two possible distances from the bulb at which you could place the lens to create a sharp image on the screen. (a) Derive an equation for the distance z between the two positions that includes only d and f. (b) Use this equation to show that the distance d between an object and a real image formed by a converging lens must always be greater than or equal to four times the focal length f.Another example (?) What is the equivalent focal length of two lenses in ContactCombination of Thin Lenses, example: final the final image.Optical instrument: magnifier.Size of an object or an imageThe size of an object (image) is preserved (determined) through the lateral angle it opens in front of our eyes.To magnify an object, one needs to create an image of it that the angle of the image is larger than that of the object.The ratio of these two angles is called the angular magnification.angle with lensangle without lensoθmθ� =Magnifying an object with a single lens: reading glasses case.Another magnifier: the compound MicroscopeTwo converging lenses make up a compound microscope. Gives much greater magnification than a single lensThe objective lens has a short focal length, ƒo< 1 cmThe eyepiece has a focal length, ƒe of a few cmHow a compound microscope worksThe lenses are separated by a distance LL is much greater than either focal lengthThe object is placed just outside the focal point of the objective This forms a real, inverted imageThis image is located at or close to the focal point of the eyepieceThis image acts as the object for the eyepieceThe image seen by the eye, I2, is virtual, inverted and very much enlargedMagnifications of the Compound MicroscopeThe lateral magnification by the objective isMo = - L / ƒoThe angular magnification by the eyepiece of the microscope isme = 25 cm / ƒeThe overall magnification of the microscope is the product of the individual magnifications25 cmƒ ƒo eo eLM M m� �= =-� �� �Another optical instrument: the telescopesTelescopes are designed to aid in viewing distant objectsTwo fundamental types of telescopesRefracting telescopes use a combination of lenses to form an imageReflecting telescopes use a curved mirror and a lens to form an imageTelescopes can be analyzed by considering them to be two optical elements in a rowThe image of the first element becomes the object of the second elementHow a refracting telescope worksThe two lenses are arranged so that the objective forms a real, inverted image of a distant objectThe image is formed at the focal point of the eyepiecep is essentially infinityThe two lenses are separated by the distance ƒo + ƒe which corresponds to the length of the tubeThe eyepiece forms an enlarged, inverted image of the first image The angular magnification depends on the focal lengths of the objective and eyepieceThe negative sign indicates the image is
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