Phtgraphic camera. Hw it wrks? Take a simple cnverging lens: Image real, inverted, and much smaller than the bject Lens Object usually at a distance much, much larger rm the lens than its cal length
T make a camera, we put the lens at the rnt side a black bx, and then we put a piece phtgraphic ilm, r a mdern CCD image cnverter where the image rms. Such a camera really can take pictures!
Fcusing a camera: Nw, i the bject were mved clser t the camera, the image wuld rm behind the ilm (r the imaging device) The ilm/imaging device shuld be mved backwards, t the psitin where the image rms, right? Hwever, mre ten it is being dne nt by mving the ilm, but mving the lens rward, instead.
Magniying glass the simplest all ptical devices
The magniying glass is just a single cnverging lens. We place the bject smewhat clser than the cal distance, and we We bserwe the virtual image by eye.
Anther graph depicting the same situatin as in the preceding slide: (but shwing, in additin, the psitin the bserver s eye).
Our eye is right behind the lens. x i x We want the image t be at a distance abut 25 cm rm the eye; this is the s-called near pint, a distance at which we put small bjects when we want t see them best, S, x is x i is the cal length. x i - 25 cm (minus, s that x because the image is 25 cm virtual); 25 cm
h i Frm the preceding h slide : x i x x 25 cm h is the bject vertical size, h graph abve it is clear that hi h - the image's vert.size. hi "Magniying Pwer" we deine as MP h x x 25 cm x 25 cm 25 cm 25 cm therere MP 25 cm i i ; rm the Practical rmula r magniying MP pwer (MP) : 25 cm [in cm]
Optical pwer : deinitin a diptre, r dipter: A diptre, r dipter, is a unit measurement the ptical pwer a lens r curved mirrr, which is equal t the reciprcal the cal length measured in metres (that is, /metres). It is designated by the Greek symbl δ : Therere, r a [in meters] magniying glass : MP 0.25 m [in meters] 4 Practical example: cal length 5 cm crrespnds t hw many diptres? What s the MP such lens? (slve n the blackbard).
The imprtance angular magniicatin: Angular size (diameter), a.k.a. aparent size, r visual angle explanatin, and cmparisn with the actual size is given in this Wiki article. T give yu an idea: Angular size : a nickel (5 cents) viewed rm the distance 3 eet; Angular size arc-minute: 0.0 inch bject rm the same distance; Angular size arc-secnd: a dime viewed rm the distance mile.
Everybdy knws this cnstelatin, right? This is Ursa Majr, in Latin: the larger emale bear (there is als a smaller ne). The highlighted seven stars rm the Big Dipper
Seven stars in Big Dipper? N! Thusands years ag it was knwn that the uppermst star in the grup, called Mizar, has a cmpanin, a smewhat dimmer star. The smaller star was given a name Alcr. The angular size the Mizar-Alcr pair is abut 2 minutes arc. Peple with gd eyes can see that it is a pair, nt a single star. It was used as an eye-test by the ancient armies. Using even a small telescpe, ne can clearly see that Mizar and Alcr rm a binary star system. They rbit the cmmn center mass, ne cycle last abut 750,000 years.
Arund the year 650, shrtly ater Galile built his irst telescpe, it was discvered that Mizar is nt a single star, but a system tw! The angular size the Mizar A and Mizar B system is nly 4 secnds arc, almst 60 times less then the Mizar-Alcr angular size. By the end the XIX century astrnmers und much evidence that bth Mizar A and Mizar B have smaller cmpanins. S the whle system is actually a Quintuple ne!
Hwever, the irst direct bservatin the Mizar A cmpanin was made nly in 996, using an extremely pwerul instrument that can see bject angular size as small as 0.00 secnd arc!
The angular size the Mizar-Alcr pir, 2 minutes arc, is mre r less the limit human eyesight. State--the-art instruments nw can see bjects with angular size as small as 0.00 secnd arc which crrespnds t angular magniicatin nearly ne millin! The simplest ptical instrument that magniies the angular size distant bject is a reracting telescpe, cnsisting just tw lenses. Histrically, the irst telescpe used r astrnmical bservatin was built by Galile in 609. It used a cnvex bjective lens, and a diverging lens as the eyepiece. In 6 Kepler invented anther type that uses tw cnvex lenses. The Keplerian telescpe became ar mre ppular than the Gallilean ne, and is still widely used tday s we will discuss nly the Kepler s design.
Cnsider a pair distant stars that tgether rm an bject angular size α. It is easy t cnstruct the image such bject rmed by a cnverging lens. Stars ar, ar away The rays rm a very distant pint bject are nearly parallel, s that the image is a pint lcated at the cal plane. The ray-tracing is very simple, it s enugh t draw just a single ray r each star the ne passing thrugh the lens center.
The images rmed n the cal plane are real images. Real images, as we knw, can be viewed n a screen. But we will nt use a screen we want t get a magniied image! Therere, we will use anther lens, the eyepiece, which will act as a magniying glass. Simple idea? Surely! Nw, let s think. It s quite clear that we want t get a magniicatin as big as pssible. And hw we use a magniying glass t get the best pssible magniicatin? Let s make a small break nw, and let s switch r a mment t the Java Lens Tutrial.
Back t the slides. We have rereshed ur memry with the Java tutrial : One gets the best magniicatin by placing the bject just behind the cal pint the magniying glass (belw, marked as F e ). Our bjects r the magniying glass i.e, the eyepiece lens are the star images that rmed n the cal plane the bjective. Again, we can use A simpliied single-ray ray-tracing prcedure, t btain the angular size β the star pair image seen thrugh the eyepiece lens.
T ind the angular magniicatin a Keplerian Telescpe, we will use the same ray tracing scheme as in the preceding slide. Hwever, in rder t acilitate the calculatin, we will place ne the stars exactly n the instrument s axis*: * α * * * β One can always d that by aiming the telescpe in such a way that ne the stars is exactly in the center the visin ield.
Nw, a tiny bit trignmetry. Fr small angles, the tangent is, t a very gd apprximatin, equal t the angle. tan AB AO AB Angular magniicatin ; M ang tan e AB AO AB AB AB e e α α O O A B * * β β M ang e Objective cal length Only slightly less than e