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Unformatted text preview: Optical systems 5.2 Optical Instruments • Optical Instruments –the eye –cam era –Magnifi ers and m icroscopes –Tel escopes • For system s of several m irrors and lenses the im age formed by one element serves as the object for the ne xt element. Camera The cam era form s a real inverted im age of an object at the im age plane of the film (digital light sensors) Limitations of Lens • Spherical aberration • Chromatic aberration • Fnumber Spherical Aberration Chromatic Aberration nonparaxi al rays paraxi al rays 1 fnumber fnumber = Single lens reflex camera 1 m ultielem ent lens 2 m irror 3 shutter 4 film 5 focusing screen 6 lens 7 prism 8 lens f D D f “Fast” lenses with low fnum bers (1.2)are difficult to m ake and expensive because aberrati ons. Optical system for a Single lens refl ex cam era Eye Cornea, aqueous humor and lens refract light Detection at the retina. Principally at the fovea. ~1.7 cm Range of Normal Vision far point a t i nfini ty relaxed eye near poi nt ~ 25 c m ac commoda ted eye The amount of light entering the eye is regulated by the size of the pupil which is the aperture in the iris. The eye is focused by changing the flatness of the lens, in a process called accommodation. The rel axed eye can focus on an object at infinity (far point) The accomm odated eye can focus on an object at 25 cm (near point) The near point and the far point can vary in different individual s and can change with age. Defects in vision Nearsight edness and farsightedness – due to the mism atch between the focal l ength of the eye and the distance between lens and retina. Power of a corrective lens Prescription eyeglass lenses are specified by the power P P = 1 f 1 Units of m or diopters 2 Farsightedness Lack of near vision 25 cm Correcting farsightedness 25 cm unfoc used foc used Farsight ed eye cannot focus on an object at the near point of a norm al eye. The lensretina distanc e is too short and/ or the l ens is not convergent enough. The light is m ade to converge m ore by using a converging l ens. Nearsightedness lack of far vision Normal eye foc uses at infi nity Correcting nearsightedness unfoc used foc used Nearsight ed eye cannot focus on objects far away (further than the far point < infinity) The lens retina distanc e is too long and/ or the lens is too converging. Nearsight ed visi on can be corrected by using a diverging lens ( m aking the light less convergent). Example A farsight ed person has a near point of 50 cm. W hat power lens will correct this to norm al vision. (ignore the distance between the lens and the eye. unfocused focused 25 cm 50 cm object virtual im age Use a l ens that can take an object at 25 cm and form a virtual im age at a distanc e of 50 cm. f= ll ' ( 25)( -50 ) = = +50cm = 0.50m l + l ' 25 - 50 Example A nearsighted person has a far point of 25 cm. W hat power lens will correct this to norm al vision. (ignore the distance between the lens and the eye. unfocused focused 25 cm object virtual im age Use a l ens that can take an object at infinity and form a virtual im age at 25 cm. 1 1 1 += l l ' f 1 1 1 + = ¥ -25 f P= 1/0.5m =2.0 diopters A converging l ens A diverging lens 1 = -4.0 diop ter s -0. 25 f=25 cm =0.25m P= 3 Magnifiers How do we image small objects? • W e can im age a sm all object by bringing it close t o our eye. • But we cannot bring it closer than the near point. (we can’t focus on it). • Alternativel y we can produc e a l arger im age of the object at the near point (or farther away) that can be focused on by the eye. Angular magnification Naked eye Angle subtended by the object (sm all angl e approx. radians) a=
W ith m agnifying lens h 25cm h f b= If f is sm aller than 25 cm the im age will be m agnifi ed. You can bring the object close to the eye. m = b 25cm = a f Question What a magnifying glass with a focal length of 10 cm is used. W hat is the magnification? Compound Microscope A compound m icroscope magnifies the im age of small objects using 2 lenses. • Objective lens forms an enlarged real im age • Eyep iece lens forms an enlarged virtual im age that is visualized by the eye. (as with the m agnifying glass) Compound Microscope (not to scale) Enlarged real im age due to Obj ective Enlarged virtu al im age due to Eyepiece Question Find the m agnification of a com pound m icroscope with focal lengths for the objective and eyepiec e of 6.1 mm and 1.7 mm respectivel y and the l enses are 8.3 cm apart? objective m agnificati on m : - (L - fe ) : - L o fo fo for L>> fo m agnifier eyepi ece m agnification Total m agnificati on m = e 25cm fe L æ 25cm ö m = - ç ÷ f è fe ø
o 4 Refracting telescope A refracting telescope collects light from distant objects and form an im age with a large angular magnification using 2 lenses • Objective lens form s a real image of the far away object near the focal length • Eyepiece views the im age like a magnifier. Refracting telescope a is the angle subt ended by light afrom the far aw ay object. b is the angle subt ended by the light through the eyepiec e angular m agnification a= h 1 fo b= h 1 fe m = b f = o a fe Telescope The Hubble space telescope has an objective m irror with a focal length of 57.8 m viewed with optics equivalent to an eyep iece with a focal length of 7.2x103 m What is the angular magnification? f 5 7.8 3 o = = 8 .0 x1 0 fe 7 .2 x10 -3 Hubble T elescope Image of M100 Spiral Galaxy (NASA) m= Limits to magnification • For refracting optics there are problems of chromatic and spherical aberration. • Problem s in precision in constructing the refracting and reflecting surfaces. • Diffraction – A basic problems having to do with the wave nature of light (discussed ne xt) 5 ...
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- Spring '09