PHYS-2020: General Physics IICourse Lecture NotesSection XIVDr. Donald G. LuttermoserEast Tennessee State UniversityEdition 3.3AbstractThese class notes are designed for use of the instructor and students of the course PHYS-2020:General Physics II taught by Dr. Donald Luttermoser at East Tennessee State University. Thesenotes make reference to the College Physics, 9th Edition (2012) textbook by Serway and Vuille.XIV. Optical InstrumentsA. Common Optical Tools.1. A ca mera consists of a lens (or series of lenses) that focus animage onto a light sensing detector (e.g., film, CCD, etc.).a) The diameter of the lens can be stopped-down to smallersizes by adjusting the aperture opening.i) These stops are technically referred to as thef-number.f-number ≡fD(XIV-1)f = focal length of lens.D = diameter of the lens or aper ture (whichever is smaller)ii) The larger the f number, the less light is allowedinto th e camera.iii) Cameras typically have th e following f-stops: f/2.8(lets the most light in), f/4, f/5.6, f/8, f/11, f/16(lets t he least amou nt of light in).b) The magnification of the image follows the thin lens for-mulae (e.g., Eq. XII-10) with an image size given byh0=hpf . (XIV-2)c) The amount of light that falls on the d etector is deter-mined by the f-stop and the shutter speed.i) For fast mov ing objects, one should use shutterspeeds 1/1000th or 1/500th of a second.XIV–1XIV–2 PHYS-2020: General Physics I Iii) For indoor, low-light levels, speeds greater than1/60th of a second are required =⇒ speeds longerthan 1/60 sec usually req uire the camera t o bemounted on a tripod to keep the camera steady.iii) Astronomical photographs typically req uire t heshutter to be open f rom minutes to hours in orderto record the image.2. The organic analogy to the camera is the eye. In the case of thehuman eye we h ave the following characteristics:a) The iris is equivalent to the apert ure of the camera =⇒the opening is called the pupil.b) The cornea is a transparent lens cap for the eye’s lens.c) The retina records the image and sends the signal to thebrain via the optic nerve =⇒ analogous t o the film in acamera or a CCD chip. The retina is composed of 2 typesof receptor cells:i) Rods are able to detect low light levels in black-and-white.ii) Cones come in 3 types that respond respectivelyto red, green, and blue light.d) Defects of the eye:i) Hyperopia: Image of a nearby object forms be-hind the retina (farsighted).ii) M yopia: Maximum focal length of eye lens isshorter than diameter of eye (nearsighted).Donald G. Luttermoser, ETSU XIV–3iii) Astigmatism:A point source prod uces a line im-age on the retin a.iv) Cataracts: Lens and/or cornea becomes par-tially or totally opaque.v) Glaucoma: Abnormal increase in fluid pr essureinside the eyeball.e) Corrective lenses are often used to correct many defects ofthe eye. The po wer of such a lens is measured in diopters:P(diopters) =1f(m)(XIV-3)=⇒ f is the lens focal length in meters.i) The near point is the closest distance for whichthe lens can accommodate t o focus light on theretina. This distance changes as the eye ages:Age 10: near point = 18 cm.Age 20: near point = 25 cm.Age 40: near point = 50 cm.Age 60: near point = 500 cm.ii) The far point is the farthest distance for whichthe lens of a relaxed eye can focus light on theretina. People with normal vision can focus ob-jects that are very far away (e.g., the Moon). Forthese people the far point is essentially infinity.3. The Simple Magnifier in creases the image size of an objectwith a single lens (i. e., magnifying glass), with a magnificationofm ≡θθ◦(XIV-4)XIV–4 PHYS-2020: General Physics I I=⇒ θ = angle the object su bten ds with th e lens=⇒ θ◦= angle the object subtends to th e naked eye .B. Microscopes and Telescopes.1. Both microscopes and re f racting telescopes have a series of 2 (ormore) lenses that are used to magnify an image.a) The objective lens is the light collector =⇒ the biggerthe objective, the m ore light you receive, the fainter theobject you can see.b) The eyepiece lens is the main compon ent of magnifica-tion.c) A reflecting telescope has a mirror (usually parabolicin shape) to collect the light and is called the primarymirror instead of the objective lens.2. These in struments magnify objects following the relations:a) For compound microscopes:M = M1me= −Lfo 25 cmfe!, (XIV-5)whereM1= magnification of the objectiveme= magnification of the eyepieceL = distance between objective and eyepiece (in cm)fo= focal len gth of the obj ective (in cm)fe= focal len gth of the eyepiece (in cm) .Donald G. Luttermoser, ETSU XIV–5b) For a telescope:m =fofe. (XIV-6)i) Note that one can get as high as a magnificationas you want by j ust getting eyepieces with smallerand smaller focal lengths.ii) The higher the magnification, the fainter the im-age =⇒ rule of thumb for useful magnifications: 50power f or each inch of the objective.=⇒ a 2.4” telescope’s maximum useful power is120!Example XIV–1. Problems 25.33 ( Page 882) from theSerway & Vuille te x tbook: Astronomers often take photographswith the objective lens or mirror of a tel escope alone, without aneyepiece. (a) Show that the image size h0for this telescope is givenby h0= fh/(f − p) where h is the object size, f the objective f ocallength, and p the object distance. (b) Simplify the expression in part(a) if the object distance is much greater than the objective focallength. (c) The “wingspan” of the International Space S tation is108.6 m, the overall width of its solar panel configuration. Whenit is orbiting at an altitude of 407 km, find the width of the imageformed by the telescope objective of focal length 4.00 m.Solution (a):Using the thin lens equ ation (Eq. XII-10), we get1p+1q=1f1q=1f−1p1q=ppf−fpfXIV–6 PHYS-2020: General Physics I Iq =pfp − f.Inserting this into the magnification equation (Eq. X II-11), wegetM =h0h= −qp= −fp − f.Therefore the image size will beh0= Mh = −fhp − f=fhf − p.Solution (b):If p  f, t hen f − p ≈ −p andh0≈ −fhp.Solution (c):Suppose the telescope observes the space station while at thezenith (i.e., the point directly overhead), thenh0≈ −fhp= −(4.00 m )(108.6 m)407 × 103m= −1.07 × 10−3m = −1.07 mm .C. Spatial Resolution.1. The ability of an optical system to distinguish between closelyspaced objects is limits due to the wave nature of light.a) Light gets diffracted when passing through apertures(see