Lecture 10. Lecture 10

Transcription

1 Lecture 0 Telescope [Reading assignment: Hect 5.7.4, 5.7.7] A telescope enlarges te apparent size o a distant object so tat te image subtends a larger angle (rom te eye) tan does te object. Te telescope is an aocal system, wic means tat bot te object and image are at ininity. Astronomical telescope objective eyepiece AS exit pupil Q at ininity s s tan tan s --- s Using te lens law or te eyepiece: s s s s --- s Magniication M ---- So tan tan For small angles, tan tan, ten M Te exit pupil is te image o te AS. Deine CA o entrance pupil clear aperture CA e exit pupil clear aperture From te diagram, it is clear tat Jerey Bokor, 2000, all rigts reserved

2 CA o CA e s M s Te eye is placed at te exit pupil, so a CA e muc larger tan 3 mm is not very useul. However, making it somewat larger makes it easier to align te eye to te eyepiece. Binoculars may ave CA e ~ 5 mm. Resolution Te resolution o te eye is arc min 60 arc sec. So in a telescope, te eye can resolve objects separated by an angle i Now, te diraction limit o te telescope can be written as T 5.5 CA o, wit T in sec. and CA o in inces (or 550nm wavelengt). At te diraction limit, te inest detail in te image as an angular separation o M T. I tis angle is at least 60 sec, te eye can resolve te detail. So, wit At tis magniication, te diraction limit and te resolution o te eye are equal. Magniication muc larger tan tis means tat te diraction blur spot is larger tan te smallest eature tat te eye can resolve. Te eye sees a rater blurry image. Example: 2 reractor telescope mm Galilean Telescope M -- in min M M CA max CA o o M max 28 mm objective M 28 9mm objective M 78 no increase in resolution ard to align te eye M --- is negative, so M 0. Non-inverting. 2 Jerey Bokor, 2000, all rigts reserved

3 Tis telescope would seem to be a good candidate or binoculars. Inexpensive ield glasses or opera glasses are indeed made according to tis design, but it turns out to ave a very limited ield o view Relecting Telescope main mirror eyepiece All modern astronomical telescopes ave tis basic coniguration because it is muc more practical to abricate large mirrors tan lenses. Te size o te large main mirror (te entrance pupil) sets te diraction limit. Also, a larger entrance pupil gaters more ligt, so tat aint objects can be detected. Groundbased telescopes are limited by atmosperic turbulence, wic introduces unavoidable aberrations. One solution is to go into space, above te atmospere. Te coniguration sown above, wit a parabolic mirror is called a Newtonian relector. It as airly good perormance and is inexpensive, but does suer rom coma aberration or o-axis objects. Catadioptric designs use a combination o mirrors and lenses to old te optics and orm an image. Tere are two popular designs: te Scmidt-Cassegrain and te Maksutov-Cassegrain. In te Scmidt- Cassegrain te ligt enters troug a tin asperic Scmidt correcting lens, ten strikes te sperical primary mirror and is relected back up te tube and intercepted by a small secondary mirror wic relects te ligt out an opening in te rear o te instrument were te image is ormed at te eyepiece. Te corrector lens reduces te o-axis aberrations, giving good images over a wider ield tan te Newtonian. An additional advantage is tat te lens seals te telescope tube, wic protects te primary mirror rom contamination, as well as stiening te structure. 3 Jerey Bokor, 2000, all rigts reserved

4 Te Maksutov design uses a tick meniscus correcting lens wit a strong curvature and a secondary mirror tat is usually an aluminized spot on te corrector. Te Maksutov secondary mirror is typically smaller tan te Scmidt's giving it sligtly better resolution, especially or observing extended objects, suc as planets, galaxies, and nebulae. Microscope [Reading assignment: Hect 5.7.3, 5.7.5] Simple microscope (magniier) image simple lens, object eye object located inside lens ocal lengt virtual image is ormed at s s s Simple application o te lens law gives: 4 Jerey Bokor, 2000, all rigts reserved

5 I te eye is located at te lens, te angle subtended by te image is I te eye views te same object at standard viewing distance ( cm), ten te angle would be Te magniier enlarges te object by te ratio One may adjust te lens to put te image appearing at relaxed eye, ten Wit te image appearing at cm (standard viewing distance), ten Compound Microscope s s s s M objective s s M M s x s 2 d s in cm s, wic means tat it is viewed wit a ully eyepiece Te objective lens produces a real (inverted), magniied image o te object. Te eyepiece re-images to a comortable viewing distance and provides additional magniication. Te total magniication is te product o te linear objective magniication times te eyepiece angular magniication. s M o s M e M TOT M o M e x x Jerey Bokor, 2000, all rigts reserved

6 In laboratory microscopes, x is called te tube lengt and is standardized to 60 mm. So, te objective 6 magniication is given by M o Tus, a 20objective lens as a ocal lengt o 0.8 cm. Resolution. Te aperture stop is usually set by te size o te objective (NA). Recall tat te diraction limited linear resolution is 0.6 Z Tis is te smallest object tat can be resolved. NA Te eye can resolve an object size o ~0.08 mm at te distance o cm, so te equivalent object size in te microscope is R mm M Te magniication at wic tese two resolutions are equal is Take 0.55m M max 240NA mm M NA M NA NA 0.6 wit in mm Increasing te magniication beyond tis does not allow observation o smaller objects due to diraction. 6 Jerey Bokor, 2000, all rigts reserved