Laws of lenses and optical instruments TEP

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1 aw o lene and optical intrument TEP Related Topic aw o lene, maniication, ocal lenth, object ditance, telecope, microcope, path o a ray, convex len, concave len, real imae, virtual imae. Principle The ocal lenth o unknown lene are determined by meaurin the ditance o imae and object and by Beel method. Simple optical intrument are then contructed with thee lene. Equipment en, mounted, = +0 mm en, mounted, = +50 mm en, mounted, = +00 mm en, mounted, = +300 mm en, mounted, = 50 mm en, mounted, = 00 mm Screen, tranlucent, mm Screen, with arrow lit Ground la creen, mm Double condener, = 60 mm Stae micrometer, mm - 00 div Do lea, Ctenocephalu, mip Slide -Emperor Maximilian Optical proile-bench, l = 000 mm Bae. opt.proile-bench, adjut Slide mount. opt.pr.-bench, h = 30 mm Slide mount. opt.pr.-bench, h = 80 mm Diaphram holder en holder Condener holder Swinin arm Experiment lamp 5, with tem 60-0 Power upply 0- V DC/6 V, V AC Connectin cord, l = 500 mm, blue Rule, platic, l = 00 mm Tak. To determine the ocal lenth o two unknown convex lene by meaurin the ditance o imae and object.. To determine the ocal lenth o a convex len and o a ination o a convex and a concave len uin Beel method. 3. To contruct the ollowin optical intrument:. Slide projector; imae cale to be determined. Microcope; maniication to be determined 3. Kepler-type telecope 4. Galileo telecope (opera lae). Set-up and procedure The experiment i et up a hown in Fi.. A parallel liht beam i produced with the lamp and the double condener.. The object (creen with arrow lit) i directly behind the condener, and a clear imae i projected on to the creen with a len. The ditance o imae and object rom the len are meaured (aume that the lene are thin). The meaurement o ditance o imae and object i repeated, uin both lene and with the len and the creen in dierent poition. P000 PHYWE Syteme GmbH & Co. KG All riht reerved

2 TEP aw o lene and optical intrument Fi. : Experimental et-up (microcope).., at a ixed ditance d between object and imae (cae ), we alter the poition o the len o that the imae and object ditance are tranpoed (cae ), we till obtain a clear imae o the object. n cae the imae i maniied, in cae it i reduced (Fi. ). Fi. : Determination o ocal lenth ater Beel. Uin a convex len o ocal lenth +00 mm, or intance, meaure the ditance e at which a harp imae i obtained or both poible len poition (repeat the meaurement and calculate the averae value e. Now take a meaurement in the ame way but uin the convex len rom the irt meaurement and a concave len (-00 mm or example). Make the ditance d a lare a poible, and meaure at leat our time the ined ocal lenth. 3.. Slide projector Place the lide Emperor Maximilian immediately behind the condener and project an imae on the creen with the len ( = +00 mm). PHYWE SYSTEME GMBH & Co. KG All riht reerved P000

3 aw o lene and optical intrument TEP To obtain the bet imae illumination et the condener o that the imae o the lamp coil i in the plane o objective len (Fi. 3). Determine the maniication M o the imae M B G Fi. 3: Path o a ray in a lide projector. 3. Microcope A maniied imae o a mall object (tae micrometer and micro-lide o a do lea) i produced with a len o hort ocal lenth = +0 mm. The real intermediate imae i oberved throuh an eyepiece ( = +50 mm) (Fi. 4). The round la and the object holder with the object are ixed in the winin arm. i brouht a cloe to the object a poible. The object i illuminated throuh a round la creen. The ie o the imae and thence the overall maniication are rouhly determined by comparin it with a cale at the leat ditance o ditinct viion (approximately 5 cm). To do thi we look throuh the microcope with the riht eye and at the cale with the let. With practice the two imae can be uperimpoed. Fi. 4: Path o a ray in the microcope. P000 PHYWE Syteme GmbH & Co. KG All riht reerved 3

4 TEP aw o lene and optical intrument 3.3 Telecope ater Kepler A convex len o lon ocal lenth (+300 mm, or example), and one o hort ocal lenth (e mm) are ecured to the optical bench at a ditance o + (Fi. 5). Fi. 5: Path o a ray in a Kepler telecope. we look throuh the len o hort ocal lenth, we can ee an inverted, maniied imae o a ditant object. 3.4 Galileo telecope (opera lae) A convex len o lon ocal lenth (+300 mm, or example) and a concave len o hort ocal lenth (e mm) are et up at a ditance o (Fi. 6). Throuh the concave len we can ee ditant object maniied and the riht way up. Fi. 6: Path o a ray in Galileo telecope. Theory and evaluation The relationhip between the ocal lenth o a len, the object ditance and the imae ditance b i obtained rom eometrical optic. Three particular ray, the ocal ray, the parallel ray and the central ray, are ued to contruct the imae (Fi. 7). Fi. 7: mae contruction with three principal ray. 4 PHYWE SYSTEME GMBH & Co. KG All riht reerved P000

5 aw o lene and optical intrument TEP From the law o imilar trianle, B b G and G B b where B i the imae ie and G i the object ie. By tranormin we obtain the len ormula b or b b. From the value o b and meaured in Tak we calculate, the averae value o and it tandard deviation. For the irt len (00 mm) wa 00. mm with a tandard deviation o 0.6 mm; or the econd (50 mm), wa 53. mm with a tandard deviation on the lene have a tolerance o 5%.) o 0.9 mm. (The ocal lenth marked. Since b (the object ditance in cae = imae ditance in cae ) and ince b, b b d e (ee Fi. ). we olve the equation or and b we obtain ( d e) b ( d e Subtitutin into the len ormula ive ) d e 4d The ocal lenth o the convex len can thereore be determined rom the meaured value o d and e. we now ue a len ytem o ocal lenth. Conitin o the convex len already meaured (ocal lenth ) and a concave len, and carry out the meaurement in the ame way, we obtain the ollowin or the ocal lenth o the concave len : or P000 PHYWE Syteme GmbH & Co. KG All riht reerved 5

6 TEP aw o lene and optical intrument Here we aume that a otherwie no real imae would be produced. wa 99.7 mm or the convex len (+00 mm),. wa 80 mm or the ination o two lene (+00 mm/-00 mm) o that = -3 mm repreent the ocal lenth o the concave len. (The ination o two lene involve a ytematic error a the ditance between the principal plane i direarded). 3. The maniication M i obtained rom the relationhip between object ie and imae ie b M B G b When the imae ditance b i 700 mm and the ocal lenth =00 mm, then M = The overall maniication i obtained by multiplyin the maniication due to the objective (Fi. 4), ß objective Y' Y a' a' by the anular maniication o the eyepiece 50mm With the lene ued we obtain an overall maniication M = The objective provide a real, inverted imae o ie Y o a very ditant object, and thi imae i oberved throuh the eyepiece. The anular maniication (or mall anle) i ' Y' / Y' / 3.4 A concave len i placed in the path o the ray in ront o the real irt imae produced by objective o that the ocal point F and F coincide. The eye then ee a virtual, upriht imae. The maniication i once aain Note You may wih to cover the markin on the lene ued to meaure ocal lenth by mean o opaque adheive tape while perormin the experiment, and reveal thee value only when the evaluation i inihed. 6 PHYWE SYSTEME GMBH & Co. KG All riht reerved P000

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