15.2 Optical Instruments• Simple magnifier• Compound microscope• TelescopeMagnifiersHow do we image small objects?• We can image a small object by bringing it close to our eye.• But we cannot bring it closer than the near point. (we can’t focus on it).• A magnifier can produce a larger image of the object at the near point (or farther away) that can be focused on by the eye.• Key concept -Angular magnificationAngular size25 cmθObjects closer than the near point are not in focus. Punfocusedimage onretinaNot to scaleThe angle θ increases as p decreasesThe image size increasesSimple Magnifier25 cmhA converging lens in combination with the lens of the eye forms an image on the retina from an objectcloser than the near point of the eye.Ignore the distancebetween the lens and the eyeHow does it work?Produces an enlarged virtual image at a distance fromthe eye (from 25 cm to infinity) that the eye can focus on.25 cmf•objectvirtualimageθSimple Magnifierpqh’hθ IncreasesAngular MagnificationThe angular magnification is the ratio of θ for the magnified image compared to value of θofor the object at the nearpoint of the eye. (25 cm) 25 cmf•objectvirtualimageθh’homθ=θMagnified25 cmθohUnmagnified2Angular magnificationThe angular magnification for the simple magnifier can have a range of values because the focal length of the eye can vary due to accommodation.The simplest case is the magnification for the relaxed eye. (focused at infinity)Object at the focal point. p = fImage at - infinity q = - infinitySimple Magnifier25 cmf•objectθpq = -infinityhhtanfθ=hfθ≈for small anglestan θ ~ θThe linear magnification is infinite (not useful) but the angular size is well defined.What is the value of θ ?Simple Magnifier25 cmf•objectθpq = -infinityhhfθ≈25 cmθohUnmagnifiedWhat is the Angular Magnification?oh25cmθ≈Angular magnification025cmmfθ==θf is the focal lengthof the lens in cm.Simple magnifier.A simple magnifier with a focal length of 5.0 cm is used to view an insect. What is the angular magnification for a relaxed eye?25cm 25cmm5.0f5.0cm== =Simple magnifiers.The angular magnification for a single lens is limited by aberration to about 4. Combination lenses can have magnification to about 20.Compound Microscopes.Magnification by 2 lenses.Objective lens – Produces an enlarged real image of the object.Eyepiece – Used like a simple magnifier to view the image.The net angular magnification of the product of the two magnifications.3Compound microscopeEyepieceObjectiveCompound microscopeMaNot to scaleThe objective lens produces a magnified real image I1The image is viewed through the eyepiece.Compound microscopeMaNot to scaleThe objective lens produces a magnified real image I1The image is viewed through the eyepiece.1o1oqLMpf=− ≈−ee25cmmf=For relaxed eyeMagnification1eoeL(25cm)mMmff==−Overall angular magnificationMagnification increases when feand feget smaller.MagnificationA compound microscope has an objective lens and eyepiece with a focal lengths of 1.5 cm and 2.0 cm respectively. The microscope is 20 cm long. Find the angular magnificationoeL (25cm) 20 (25cm)m 167ff 1.52.0=− =− =−Refracting TelescopeTwo lensesObjective lens – produces a reduced imageof a distant object near the focal point.Eyepiece – used to magnify the image.4telescopeAngular magnificationooefmfθ==θeh'fθ=ooh'fθ=focus at infinityTelescopeThe Hubble space telescope has an objective mirror with a focal length of 57.8 m viewed with optics equivalent to an eyepiece with a focal length of 7.2x10-3m What is the angular magnification?3o3ef57.8m8.0x10f7.2x10−== =Hubble Telescope Image of M100 Spiral Galaxy (NASA)Limits to magnificationWhy can’t we use light microscopes to see atoms?• For refracting optics there are problems of chromatic and spherical aberration.• Problems in precision in constructing therefracting and reflecting surfaces.• Basic problems having to do with the wavenature of