leins

taal ka chitr
taal ka upayog prakaash ko focus karne ke liye kiya ja sakta hai

taal (leins) ek prakaasheeya yukti hai jo prakaash ke apavartan ke siddhaant par kaam karta hai. taal goleeya, belanaakaar aadi jaise niyamit, jyaamiti roop ki do satahon se ghira hua paaradarshak maadhyam, jisse apavartan ke pashchaat kisi vastu ka vaastavik athva kaalpanik pratibinb banta hai, taal kahalaata hai. uttal (convex) taal masoor ki aakruti ka hota hai.

taal ki satah praaya: goleeya (spherical) hoti hai, parantu aavashyakataanusaar belanaakar, ya agoli taal bhi prayukt hote hain. aaainkh ke kristaleeya taal hi ekamaatr praakrutik taal hai. hajaaron varsh pehle bhi log taal ke vishay mein jaante the aur maaisanar (Meissner) ke anusaar praacheen kaal mein bhi chashme se laabh uthaaya jaata tha. chashmein ke alaava prakaashavijnyaaan mein taal ka upayog dooradarshi, sookshmadarshi, prakaashastanbh, dvinetri (baainaukyular) ityaadi mein hota hai.

anukram

vargeekaran

abhisaari taal
1 - uttalottal ya dvi-uttal taal
2 - samatalottal taal
3 - uttalaavatal (abhisaari meniskas)
apasaari taal
4 - avatalaavatal ya dvi-avatal taal
5 - samatalaavatal taal
6 - abhisaari meniskas

taal ko mukhya roop se do vargon mein vibhaajit kiya ja sakta hai,

  • uttal taal (convex lens) aur
  • avatal taal (concave lens)

anant se aanevaali samaantar kiran uttal taal mein apavartan ke pashchaat bindu f par abhisrit (converge) hokar vahaaain vaastavik pratibinb bana rahi hai; jabki avatal taal mein apavartan ke pashchaat ve bindu "f" par bane kaalpanik pratibinb se apasaarit (diverge) hoti prateet hoti hain. at: uttal taal ko 'abhisaari taal' aur avatal taal ko 'apasaari taal' bhi kehte hain. yahaaain yeh jaan lena aavashyak hai ki uttal taal abhisaari taal aur avatal taal apasaari taal ke roop mein tabhi kaam karta hai, jab uske chaaron taraf ke maadhyam ka apavartanaank (refractive index) taal ke maadhyam ke apavartanaank se kam hota hai. (kaach ka apavartanaank, myoo (m) = 1.5, hava ka apavartanaank, myoo (m) = 1.00 hota hai). yadi chaaron taraf ke maadhyam ka apavartanaank taal ke maadhyam ke apavartanaank se adhik hoga, to uttal taal apasaari aur avatal taal abhisaari ho jaaega.

taal ke upayog

  • prakaasheeya yantron (camera, dooradarshi, sookshmadarshi aadi) mein
  • aaainkh ke chashmon mein
  • prakaash ko abhikendrit karne ke liye

taal nirmaata ka sootr (Lensmaker's equation)

kisi taal ki focus doori nimnalikhit sootr se nikaali ja sakti hai. is sootr ko taal-nirmaata ka sootr kehte hain.[1]

jahaaain

taal ki focus doori hai.
taal ke padaarth ki apavartan gunaank (refractive index) hai.
prakaash ke srot ke nikat vaale taal ke tal ki vakrata trijya (radius of curvature),
prakaash ke srot se door vaale taal ke tal ki vakrata trijya (radius of curvature),
taal ki motaai

patale leinson ke liye sameekaran

yadi d ka maan R1 aur R2 ki tulana mein chhota ho to ise 'patala taal' kaheinge. iske liye focus doori ka sootr is prakaar hoga (lagbhag)

[2]

yaugik taal (compound lens)

leinson mein prakaasheeya varn-vipthan ki samasya paayi jaati hai. bahut si sthitiyon mein do poorak varn-vipthan vaale leinson ke sanyog se is samasya ko bahut seema tak hataaya ja sakta hai. yadi alag-alag aakaar ke evam alag-alag padaarth ke saral leinson ko ek ke baad ek kram mein lagaaya jaaya to ise yaugik taal kehte hain.

sabse saral sthiti vah hai jismein taal ek doosare ke satakar rakhe jaanya. yadi f1 aur f2 focus doori vaale do patale taal sataakar rakhe jaate hain to unki sammilit focus doori f ka maan nimnalikhit sootr se nikaala jaayega-

choonki 1/f ko taal ki shakti kaha jaata hai, isaliye kaha ja sakta hai ki yugmit karne par leinson ki shaktiyaaain bhi jud jaati hai.

kintu yadi do patale taal paraspar d doori par rakhe jaanya to sanyukt taal tantr ki focus doori is sootr se niklegi-

taal ka nirmaan

chashma

chashmein ka taal patala hota hai aur ise bhi pehle bataai hui reeti se hi banaate hain. parantu iski satah ka utana yathaarth hona aavashyak naheen hai jitna un leinson ki satah ka jo dooradarshi aur fotograafi mein prayukt hote hain. taal ke kinaaron ko patthar ke pahiye par ghiskar chashmein ke frem ke aakaar ka bana lete hain.

nikat drushti dosh (short sight or myopia) ko door karne ke liye avatal taal aur door drushti dosh (long sight or hypermetropia) ko door karne ke liye uttal taal prayukt hota hai. abindukata (astigmatizm) ke dosh ko door karne ke liye belanadaar taal prayukt hota hai. yadi is dosh ke saath saath nikat drushti, ya door drushti, ka dosh bhi ho, to goleeya belanaakaar taal (spherocylindrical lens) prayukt hota hai. oordhvaadhar aksh (vertical axis) ki disha mein aise leinson ki shakti, kshaitij aksh (horizontal axis) ki disha mein taal ki shakti se, bhinn hoti hai.

dvifokasi taal (Bifocal Lens)

jaraadoor drushti (presbyopia) ke dosh ko door karne ke liye dvifokasi taal kaam mein aata hai, jismein avatal tatha uttal ek hi taal mein donon tarah ke taal sanyukt rahate hain. oopar ka bhaag door ki vastuon tatha nichla bhaag paas ki vastuon ka dekhne ke liye hota hai. kaaainch ko ek vishesh prakaar ki machine par ghiskar dvifokasi, taal taiyaar karte hain. aaj kal praaya: donon tarah ke leinson ko ek bhatthi mein garam kar tatha jodkar baaifokal taal banaaya jaata hai aur is tarah se banaae gaye taal sanleen dvifokasi taal (Fused bifocal lens) kahalaate hain.

sampark taal (Contact Lens)

kuchh log, jaise abhineta, sundarata ki raksha ke liye chashma naheen lagaana chaahate. unki aaainkh mein ek patala taal laga diya jaata hai, jo svachhamandal par theek baithata hai. taal aur aaainkh ke beech ka sthaan ek upayukt drav se bhar diya jaata hai. svachhamandal ke shankvaakaar ho jaane, ya sikud jaane par bhi sampark taal lagaaya jaata hai. sampark taal lagaane ke liye bahut hi saavadhaani evam dhan ki aavashyakta hoti hai.

frenel taal (Fresnel Lenses)

prakaash stambh (light houses) ke taal bahut bade aur mote hote hain. itna bada aur mota taal pehle bataai gayi reeti se banaana sambhav naheen hai. doosare, taal bada tatha mota hone ke kaaran itna bhaari ho jaata hai ki itna bhaari taal banaana bhi uchit naheen hai. san 1820 mein ogastin frenel (Augustin Fresnel) ne prakaashastanbh mein prayukt honevaale leson ke banaane ki vidhi batalaai. uchit vakrata ki, kaaainch ki chhadon ko alag alag ghisa aur chamakaana kiya jaata hai. fir unhein ek dhaatu ke frem mein silsilevaar jodkar prakaashastanbh ka taal banaaya jaata hai.

kabhi-kabhi kaaainch ko galaakar tatha saaainche mein dhaalakar bhi frenel taal banaae jaate hain. aise taal punjaprakaash (flood lights), rel maarg (rail road), yaataayaat sanket (traffic signal) ityaadi mein prayukt hote hain. san 1945 ke baad plastic padaarthon ko galaakar patale frenel taal bhi banaae gaye, jo praaya: abhikshetr (fieled) taal ke roop mein prayukt hote hain.

patale taal se pratibimb nirmaan ka simuleshan

sandarbh

  1. Greivenkamp, p.14; Hecht §a6.1
  2. Hecht, § 5.2.3

inhein bhi dekhein

  • darpan
  • prakaasheeya yantr
  • prakaasheeya avayavon ka nirmaan evam pareekshan (Fabrication and testing of optical components)

baahari kadiyaaain

simuleshan (Simulations)