c`v_©weÁvb

BDwbU 10 c„ôv # 217

BDwbU t 10

Av‡jvi cÖwZmiY

REFRACTION OF LIGHT f‚wgKv

Av‡jv †h gva¨‡gi ga¨ w`‡q Mgb Ki‡Z cv‡i Zv‡K Av‡jvK gva¨g ev ¯”Q gva¨g e‡j| Av‡jv ‡h †Kv‡bv ¯”Q I

mgmZ¡ gva¨‡gi ga¨ w`‡q mij‡iLvq P‡j| GK ¯”Q gva¨‡gi ga¨ w`‡q hvIqvi mgq Ab¨ GKwU ¯”Q gva¨‡g evav

†c‡j Av‡jv wØZxq gva¨‡g cÖ‡ek K‡i Ges wØZxq gva¨‡gi ga¨ w`‡q GKBfv‡e mij‡iLv eivei Pj‡Z _v‡K|

wKš‘ `yB ¯”Q gva¨‡gi we‡f` Z‡j Av‡ji MwZ c_ cwiewZ©Z nq| GB NUbv‡K ejv nq Av‡jvi cÖwZmiY| Av‡jvi

wewfbœ Kvh©vejxi g‡a¨ GKwU n‡jv Av‡jvi cÖwZmiY| GwU GKwU ¸iæZ¡c~Y© NUbv|

Av‡jvi cÖwZmiY ag© bv _vK‡j Avgiv evZv‡mi g‡a¨ wKQz †`L‡Z †cZvg bv, cvwbi g‡a¨ wKQz †`L‡Z †cZvg bv|

Kv‡Pi Rvbvjv w`‡q N‡i Av‡jv XzK‡Zv bv| Avgiv Pkgv w`‡q †`L‡Z †cZvg bv| Av‡jvi cÖwZmiY Avgv‡`i e¨v

e¨envwiK Rxe‡b LyeB ¸iæZ¡c~Y©| G BDwb‡U Av‡jvi cÖwZi‡Yi wbqg ev m~Îvewj, cÖwZmiYv¼, µvwšÍ †KvY, c~Y©

Af¨šÍixY cÖwZdjb cÖf…wZ wb‡q Av‡jvPbv Kiv n‡e, hv Avcbvi Rb¨ LyeB ¸iæZ¡c~Y© I AZ¨vek¨Kxq|

cvV-1 Av‡jvi cÖwZmiY (Refraction of Light)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. Av‡jvi cÖwZmiY Kx Zv e¨vL¨v Ki‡Z cvi‡eb|

2. cÖwZmi‡Yi m~Îvewj ej‡Z I wjL‡Z cvi‡eb|

3. cÖwZmiYv¼ Kx Zv e¨vL¨v Ki‡Z cvi‡eb|

10.1.1 cÖwZmiY (Refraction) †Kv‡bv mgmZ¡ I ¯^”Q gva¨‡g Av‡jv mij‡iLvq P‡j| Gi MwZi †Kvb cwieZ©b nq bv| wKš‘ Av‡jv hLb

GK ¯”Q gva¨g †_‡K Ab¨ ¯”Q gva¨‡g cÖ‡ek K‡i ZLb Gi Mgb c_ †eu‡K hvq (Av‡jv j¤fv‡e gva¨g

cwieZ©b Ki‡j w`K cwieZ©b nq bv Z‡e †e‡Mi cwieZ©b nq)|

GK ¯”Q gva¨g †_‡K Ab¨ ¯^”Q gva¨‡g hvIqvi mgq `yB gva¨‡gi we‡f` Z‡j Zxh©Kfv‡e AvcwZZ Av‡jvK iwk¥i

w`K cwieZ©‡bi NUbv‡K Av‡jvi cÖwZmiY e‡j|

10.1 wP‡Î `yÕwU Av‡jvK gva¨g evqy Ges Kv‡Pi we‡f` Zj AB| cÖ_g gva¨g evqyi ga¨ w`‡q AvMZ GKwU Av‡jvK

iwk¥ PO we‡f` Z‡ji O we› yy w`‡q wØZxq gva¨g Kv‡Pi g‡a¨ cÖ‡ek Ki‡Q| wØZxq gva¨‡g iwk¥wUi MwZ c_ OQ|

cÖ_g gva¨g †_‡K wØZxq gva¨‡g cÖ‡ek K‡i PO iwk¥i AwfgyL ev MwZc_ mvgvb¨ cwiewZ©Z n‡q‡Q| bZzb MwZ c_

OQ mvgvb¨ †eu‡K †M‡Q| GwUB Av‡jvi cÖwZmiY|

cÖ_g gva¨‡gi ga¨ w`‡q AvMZ iwk¥wU‡K AvcwZZ iwk¥ Ges wØZxq

gva¨‡gi ga¨ w`‡q MgbKvix iwk¥wU‡K cÖwZmwiZ iwk¥ e‡j| yB

gva¨‡gi we‡f` Z‡j †h we› y‡Z Av‡jvK iwk¥ AvcwZZ nq Zv‡K

AvcZb we›`y e‡j| 10.1 bs wP‡Î PO AvcwZZ iwk¥, OQ cÖwZmwiZ iwk¥ Ges O AvcZb we›`y|

wPÎ t 10.1

we‡f` Z‡ji Dci AvcZb we›`y‡Z Aw¼Z j¤‡K Awfj¤ e‡j| AvcZb we›`y‡Z AvcwZZ iwk¥ I Awfj‡¤i g‡a¨

m„ó †KvY‡K AvcZb †KvY Ges cÖwZmwiZ iwk¥ I Awfj‡¤i g‡a¨ m„ó †KvY‡K cÖwZmiY †KvY e‡j| 10.1 bs wP‡Î

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 218

NON' Awfj¤, †KvY PON AvcZb †KvY Ges †KvY N'OQ cÖwZmiY †KvY| AvcZY †KvY‡K i Ges cÖwZmiY

†KvY‡K r cÖZxK Øviv wPwýZ Kiv nq|

wPÎ 10.2

10.1 bs wP‡Î †`Lv‡bv n‡q‡Q Av‡jvK iwk¥ evqy †_‡K

Kv‡Pi g‡a¨ cÖwZmwiZ nIqvq AvcwZZ iwk¥wU cÖwZmi‡Yi

ci Awfj‡¤i w`‡K †eu‡K †M‡Q| Av‡jvK iwk¥ hLb KvP

gva¨g †_‡K evqyi g‡a¨ cÖwZmwiZ nq ZLb Av‡jvK iwk¥i

Mgb c_ nq 10.2 bs wP‡Îi g‡Zv| G‡¶‡Î cÖwZmwiZ

iwk¥ Awfj¤ †_‡K ~‡i m‡i hvq|

KvP †_‡K evqy gva¨g nvjKv| cix¶v K‡i †`Lv †M‡Q Av‡jvK iwk¥ nvjKv gva¨g †_‡K Nb gva¨‡g cÖ‡ek Ki‡j

Awfj‡¤^i w`‡K m‡i hvq A_©vr AvcZb †KvY †_‡K cÖwZmiY †KvY †QvU nq| Avevi Av‡jvK iwk¥ Nb gva¨g ‡_‡K

nvjKv gva¨‡g cÖ‡ek Ki‡j Zvi MwZc_ Awfj¤ †_‡K `~‡i m‡i hvq| A_©vr AvcZb †KvY †_‡K cÖwZmiY †KvY eo

nq| GB NUbv †_‡K Av‡jvi cÖwZmi‡Yi wbqg ev m~Î cªwZwôZ n‡q‡Q|

10.1.2 cÖwZmi‡Yi m~Î (Laws of Refraction) Av‡jvi cÖwZmiY `ÕywU m~Î †g‡b P‡j G‡`i cÖwZmi‡Yi m~Î e‡j| m~Î `ÕywU n‡jv:

(1) `yB gva¨‡gi we‡f` Z‡j AvcwZZ iwk¥, AvcZb we›`y‡Z Aw¼Z Awfj¤ Ges cÖwZmwiZ iwk¥ GKB mgZ‡j

Ae¯’vb K‡i|

(2) GK †Rvov wbw`©ó gva¨g Ges wbw`©ó e‡Y©i Av‡jvi Rb¨ AvcZb †Kv‡Yi mvBb Ges cÖwZmiY †Kv‡Yi

mvB‡bi AbycvZ me© v aªæe|

A_©vr,

sinsin

ir

= GKwU aªæe (msL¨v)|

cÖwZmi‡Yi wØZxq m~ÎwU Rvg©vb weÁvbx †mœ‡ji bvgvbymv‡i †mœ‡ji m~Î bv‡g AwfwnZ nq|

AvcZb †Kv‡Yi gvb cwieZ©b K‡i i1, i2, i3…BZ¨vw` Ki‡j cÖwZmiY †Kv‡Yi gvb cwiewZ©Z n‡e| aiv hvK

cÖwZmiY †KvY¸‡jv h_vµ‡g r1, r2, r3 ... BZ¨vw` n‡jv| G‡¶‡Î †mœ‡ji m~Îvbymv‡i,

31 2

1 2 3

sinsin sinsin sin sin

ii ir r r --------- = aªæe msL¨v (μ) ... .... ..... .... (10.1)

μ GKwU MÖxK eY©, Gi D”PviY wgD|

10.1.3 cÖwZmiYv¼ (Refractive Index) †mœ‡ji m~Î †_‡K †`Lv hvq, GK †Rvov wbw`©ó gva¨g I wbw`©ó e‡Y©i Av‡jvi Rb¨ AvcZb †Kv‡Yi mvBb I cÖwZmiY

†Kv‡Yi mvB‡bi AbycvZ me© v aªæe| GB aªæe msL¨vwU‡K cÖ_g gva¨‡gi mv‡c‡¶ wØZxq gva¨‡gi Av‡cw¶K

cÖwZmiYv¼ we‡ePbv Kiv nq|

msÁv t Av‡jvK iwk¥ hLb GK ¯”Q gva¨g †_‡K Ab¨ ¯”Q gva¨‡g Zxh©Kfv‡e cÖ‡ek K‡i ZLb wbw`©ó GK †Rvov

gva¨g I wbw`©ó e‡Y©i Av‡jvi Rb¨ AvcZb †Kv‡Yi mvBb Ges cÖwZmiY †Kv‡Yi mvBb-Gi AbycvZ GKwU aªæe msL¨v

nq GB aªæe msL¨vwU‡K cÖ_g gva¨‡gi mv‡c‡¶ wØZxq gva¨‡gi cÖwZmiYv¼ ev ms‡¶‡c cÖwZmiYv¼ e‡j|

Av‡jvK iwk¥ hLb ÔaÕ gva¨g †_‡K ÔbÕ gva¨‡g cÖ‡ek K‡i ZLb ÔaÕ gva¨‡gi g‡a¨ AvcZb †KvY i Ges ÔbÕ gva¨‡gi

g‡a¨ cÖwZmiY †KvY r n‡j ÔaÕ gva¨‡gi mv‡c‡¶ ÔbÕ gva¨‡gi cÖwZmiYv¼,

sinsina b

ir

… ….. … … … (10.2)

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BDwbU 10 c„ôv # 219

Avevi Av‡jvK iwk¥ hw` ÔbÕ gva¨g †_‡K ÔaÕ gva¨‡g cÖ‡ek K‡i ZLb ÔbÕ gva¨‡gi g‡a¨ AvcZb †KvY I ÔaÕ

gva¨‡gi cÖwZmiY †Kv‡Yi gvb wecixZ n‡e A_©vr ÔbÕ gva¨‡gi g‡a¨ AvcZb †KvYwU n‡e r Ges ÔaÕ gva¨‡g

cÖwZmiY †KvYwU n‡e i| ZLb ÔbÕ gva¨‡gi mv‡c‡¶ ÔaÕ gva¨‡gi cÖwZmiYv¼ n‡e,

1 1

sinsinsinsin

b aa b

riir

ev, b μ a = 1/a μ b … … .. …… … (10.3)

mgxKiY 10.3 †_‡K †`Lv hvq ÔbÕ gva¨‡gi mv‡c‡¶ ÔaÕ gva¨‡gi cÖwZmiYv¼ ÔaÕ gva¨‡gi mv‡c‡¶ ÔbÕ gva¨‡gi

cÖwZmiYv¼-Gi wecixZ ivwk|

A_©vr evqyi mv‡c‡¶ Kv‡Pi cÖwZmiYv¼

32

n‡j, Kv‡Pi mv‡c‡¶ evqyi cÖwZmiYv¼

23

n‡e|

GKKt †h‡nZz cÖwZmiYv¼ GKB RvZxq `ywU ivwki AbycvZ, ZvB Gi †Kvb GKK bvB| D‡jøL¨ sin i ev sin r cÖ‡Z¨KwU ivwk w·KvYwgwZK AbycvZ, G‡`iI †Kvb GKK bvB|

cig cÖwZmiYv¼ (Absolute Refractive Index) t k~b¨ gva¨‡gi mv‡c‡¶ †Kv‡bv gva¨‡gi cÖwZmiYv¼ H gva¨‡gi cig cÖwZmiYv¼| A_v©r Av‡jvK iwk¥ hLb k~b¨

gva¨g †_‡K Ab¨ †Kv‡bv gva¨‡g cÖ‡ek K‡i ZLb k~b¨ gva¨‡gi AvcZb †Kv‡Yi mvBb I †mB gva¨‡gi cÖwZmiY

†Kv‡Yi mvB‡bi AbycvZ‡K H gva¨‡gi cig cÖwZmiYv¼ we‡ePbv Kiv nq|

Av‡jvK iwk¥ hLb k~b¨ gva¨g †_‡K †Kv‡bv e¯‘ gva¨‡g Zxh©Kfv‡e cÖ‡ek K‡i ZLb wbw`©ó e‡Y©i Av‡jvi Rb¨

AvcZb †Kv‡Yi mvBb I cÖwZmiY †Kv‡Yi mvB‡bi AbycvZ‡K H gva¨‡gi cig cÖwZmiYv¼ e‡j| MvwYwZKfv‡e

k~b¨ gva¨‡g AvcZb †KvY i Ges Ab¨ †Kvb gva¨g ÔaÕ †Z cÖwZmiY †Kvb r n‡j, ÔaÕ gva¨‡gi cig cÖwZmiYv¼ μ a cÖZxK Øviv cÖKvk Kiv nq| mvaviYZ evqy gva¨‡gi mv‡c‡ÿ †Kv‡bv gva¨‡gi cÖwZmiYv¼‡K H gva¨‡gi cig

cÖwZmiYv¼ wnmv‡e aiv nq|

Zvrch© t Kv‡Pi cig cÖwZmiYv¼ 1.5 ej‡Z eySvq †h k~b¨ gva¨g ev evqy gva¨g †_‡K Av‡jvK iwk¥ Zxh©Kfv‡e

Kv‡Pi g‡a¨ cÖ‡ek Ki‡j AvcZb †Kv‡Yi mvBb Ges cÖwZmiY †Kv‡Yi mvBb-Gi AbycvZ 1.5 nq|

K‡qKwU c`v‡_©i cÖwZmiYv¼

c`v_© cÖwZmiYv¼ c`v_© cÖwZmiYv¼ c`v_© cÖwZmiYv¼

µvDb KvP

1.5225 eid

1.3087 †K‡ivwmb

1.44 wd¬›U KvP

1.5875 cvwb

1.3333 wMømvwib

1.47 nxiK

2.4172 A¨vj‡Kvnj

1.3616 †ebwRb

1.50 Dc‡ii Q‡K wewfbœ gva¨‡gi njy` Av‡jvi cÖwZmiYv¼ D‡jøL Kiv n‡q‡Q| GwU †gvUvgywU fv‡e mKj `„k¨gvb

Av‡jvK iwk¥mg~‡ni (Zi‡½i) cÖwZmiYv‡¼i Mo gvbI ejv †h‡Z cv‡i| Avm‡j mKj e‡Y©i Av‡jvi cÖwZmiYv¼

mgvb nq bv| †e¸wb e‡Y©i Av‡jvi cÖwZmiYv¼ me‡P‡q †ewk Ges jvj Av‡jvi cÖwZmiYv¼ me‡P‡q Kg| wb‡Pi

Q‡K K‡qKwU c`v‡_©i wewfbœ e‡Y©i Rb¨ cÖwZmiYv¼ D‡jøL Kiv n‡q‡Q|

wewfbœ e‡Y©i Av‡jvi Rb¨ cÖwZmiYv¼

c`v_© †e¸wb Avmgvbx meyR njy` Kgjv jvj

µvDb KvP

1.5380 1.5310 1.5260 1.5225 1.5216 1.5200 wd¬›U KvP

1.6040 1.5960 1.5910 1.5875 1.5867 1.5850 nxiK

2.4580 2.4439 2.4260 2.4172 2.4150 2.4100 eid

1.3170 1.3136 1.3110 1.3087 1.3080 1.3060

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 220

mvi-ms‡ÿc:

Av‡jvi cÖwZmiY t GK ¯”Q gva¨g †_‡K Ab¨ ¯”Q gva¨‡g hvIqvi mgq `yB gva¨‡gi we‡f` Z‡j Zxh©K fv‡e

AvcwZZ Av‡jvK iwk¥i w`K cwieZ©‡bi NUbv‡K Av‡jvi cÖwZmiY e‡j|

cÖwZmi‡Yi m~Î t

(1) `yB gva¨‡gi we‡f` Z‡j AvcwZZ iwk¥, AvcZb we›`y‡Z Aw¼Z Awfj¤ Ges cÖwZmwiZ iwk¥ GKB mgZ‡j

Ae¯’vb K‡i|

(2) GK †Rvov wbw`©ó gva¨g Ges wbw`©ó e‡Y©i Av‡jvi Rb¨ AvcZb †Kv‡Yi mvBb Ges cÖwZmiY †Kv‡Yi mvB‡bi

AbycvZ me© v aªæe|

cÖwZmi‡Yi wØZxq m~ÎwU Rvg©vb weÁvbx †mœ‡ji bvgvbymv‡i †mœ‡ji m~Î bv‡g AwfwnZ nq|

cv‡VvËi g~j¨vqb -10.1

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| yB ¯”Q gva¨‡gi we‡f` Z‡j Av‡jvK iwk¥i w`K cwieZ©‡bi NUbv‡K Kx e‡j?

(K) cÖwZdjb (L) cÖwZmiY

(M) †cvjvib (N) AceZ©b

2 cvwbi mv‡c‡¶ evqyi cÖwZmiYv¼ KZ?

(K) 1.5 (L) 1.33

(M) .075 (N) 0.75

cvV-2 µvwšÍ †KvY I c~Y© Af¨šÍixY cÖwZdjb (Critical angle and Total internal reflection)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb Ñ

1. µvwšÍ †KvY Kx Zv ej‡Z I e¨vL¨v Ki‡Z cvi‡eb|

2. c~Y© Af¨šÍixY cÖwZdj‡bi e¨vL¨v w`‡Z cvi‡eb|

3. gixwPKv Ges Gi m„wó m¤úKx©q aviYvi e¨vL¨v Ki‡Z cvi‡eb|

4. AcwUK¨vj dvBevi wKfv‡e KvR K‡i Ges Gi e¨envi eY©bv Ki‡Z cvi‡eb|

10.2.1 µvwšÍ †KvY I c~Y© Af¨šÍixY cÖwZdjb

Critical angle and Total Internal Reflection Av‡jv GK ¯”Q gva¨g †_‡K Ab¨ Avi GKwU ¯”Q gva¨‡g cÖ‡ek Ki‡j, Zvi MwZ c_ cwiewZ©Z nq|

G‡K ejv nq cÖwZmiY| Avm‡j `yB gva¨‡gi we‡f` Z‡j AvcwZZ Av‡jvi m¤ú~Y© As‡ki cÖwZmiY N‡U bv, Lze

mvgvb¨ n‡jI wKQz Ask wØZxq gva¨g KZ…©K †kvwlZ Ges wKQz Ask cÖwZdwjZ n‡q cÖ_g gva¨‡g wd‡i hvq| GB

†kvwlZ Ges cÖwZdwjZ Av‡jvi cwigvY G‡ZvB Kg †h Avgiv mvaviY †¶‡Î ZvÕ MY¨ ev MÖvn¨ Kwi bv|

Av‡jvK iwk¥ hLb nvjKv gva¨g †_‡K Nb gva¨‡g cÖ‡ek K‡i ZLb me mgq wKQz cwigvY Av‡jvK iwk¥ cÖwZmwiZ

n‡eB| wKš‘ Av‡jvK iwk¥ hLb Nb gva¨g †_‡K nvjKv gva¨‡g cÖ‡ek K‡i ZLb AvcZb †Kv‡Yi gvb GKwU wbw`©ó

gvÎv AwZµg Ki‡j Av‡jvK iwk¥ Avi wØZxq gva¨‡g cÖwZmwiZ bv n‡q m¤ú~Y© Av‡Mi gva¨‡g wd‡i Av‡m|

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BDwbU 10 c„ôv # 221

Av‡jvK iwk¥ Nb gva¨g †_‡K nvjKv gva¨‡g †M‡j cÖwZmwiZ n‡q Awfj¤ †_‡K `~‡i m‡i hvq| 10.3 bs wP‡Î PO AvcwZZ Av‡jvK iwk¥ Nb gva¨g ‘a’ †_‡K nvjKv gva¨g ‘b’-†Z cÖwZmwiZ n‡q‡Q| PO iwk¥i Rb¨ AvcZb †KvY, i = PON Ges cÖwZmiY †KvY, r = MOQ| ‘b’ gva¨‡g Av‡jvK iwk¥ OQ c‡_ cÖwZmwiZ n‡q‡Q| Gici

AvcZb †KvY µgk evov‡Z _vK‡j cÖwZmiY †KvYI e„w× †c‡Z _vK‡e| Gfv‡e evo‡Z _vK‡j GK mgq Ggb

GKwU AvcZb †Kv‡Y †cŠu‡Q hv‡e hLb cÖwZmiY †KvY 90° n‡e| aiv hvK,-

AvcZb †KvY evwo‡q CON = θc Kiv n‡jv- G‡Z

cÖwZmiY †KvY MOQ' = 90° n‡jv| A_©vr cÖwZmwiZ

iwk¥wUi Mgb c_ n‡jv we‡f` Z‡ji Dci w`‡q ev Zj

†N‡l| 10.3 bs wP‡Î †`Lv‡bv n‡q‡Q OQ'| Gici AvcZb

†KvY mvgvb¨Zg e„w× †c‡j cÖwZmiY †KvY 90° †_‡KI

evo‡e, wKš‘ Zv wK m¤¢e? d‡j †`Lv hvq Av‡jvK iwk¥

cÖwZmwiZ bv n‡q m¤ú~Y©iƒ‡c cÖwZdwjZ n‡q c~e©ewZ© Nb

gva¨g ‘a’-†ZB wd‡i Av‡m| 10.3 wP‡Î AvcwZZ RO

AvcwZZ iwk¥i Rb¨ cÖwZdwjZ iwk¥ n‡e OD|

wPÎ t 10.3 µvwšÍ †KvY I Af¨šÍixY cÖwZdjb

G¶‡Î AvcZb †KvY (i) = RON Ges cÖwZdjb †KvY (r) = NOD | †KvY ywU mgvb n‡e| AvcZb †Kvb

AviI e„w× Ki‡j cÖwZdjb †KvY AviI evo‡e| Ges Gfv‡eB Pj‡Z _vK‡e| AvcwZZ Av‡jvK iwk¥ we‡f` Zj

†_‡K cÖwZdj‡bi wbqg Abymv‡i Av‡Mi gva¨‡g wd‡i Avm‡e| Av‡jvi Gfv‡e m¤ú~Y©iƒ‡c Av‡Mi gva¨‡g wd‡i

Avmvi cÖwµqv n‡jv Af¨šÍixY cÖwZdjb|

µvwšÍ †KvY (Critical Angle) t wbw`©ó e‡Y©i Av‡jvK iwk¥ Nb gva¨g †_‡K nvjKv gva¨‡g cÖwZmwiZ nIqvi mgq

AvcZb †Kv‡Yi †h gv‡bi Rb¨ cÖwZmiY †KvY 90° A_©vr GK mg‡KvY nq A_©vr cÖwZmwiZ iwk¥ we‡f`Zj †N‡l

hvq, Zv‡K nvjKv gva¨‡gi mv‡c‡¶ Nb gva¨‡gi µvwšÍ †KvY e‡j| µvwšÍ †KvY‡K mvaviYZ θc Øviv cÖKvk Kiv

nq 10.3 wP‡Î CON = θc|

c~Y© Af¨šÍixY cÖwZdjb (Total Internal Reflection) t wbw`©ó e‡Y©i Av‡jvK iwk¥ Nb gva¨g †_‡K nvjKv gva¨‡g

µvwšÍ †Kv‡Yi †P‡q eo gv‡bi †Kv‡Y AvcwZZ n‡j Av‡jvK iwk¥ cÖwZmwiZ bv n‡q yB gva¨‡gi we‡f` Zj †_‡K

cÖwZdj‡bi wbqg Abymv‡i m¤ú~Y©iƒ‡c Nb gva¨‡gi Af¨šÍ‡i (Av‡Mi gva¨‡g) wd‡i Av‡m| Av‡Mi gva¨‡g wd‡i

Avmvi GB cÖwµqv‡K Af¨šÍixY cÖwZdjb e‡j|

nxi‡Ki µvwšÍ †KvY 24° ej‡Z eySvq nxiK †_‡K evqy ev k~b¨ gva¨‡gi we‡f` Z‡j 24°†Kv‡Y AvcwZZ Av‡jvK

iwk¥i cÖwZmiY †KvY 90° n‡e, A_©vr cÖwZmwiZ iwk¥ we‡f` Zj †N‡l cÖwZmwiZ n‡e| AvcZb †Kv‡Yi gvb 24° †_‡K †ewk n‡j Av‡jvK iwk¥i cÖwZmiY bv n‡q c~Y© Af¨šÍixY cÖwZdjb n‡e|

g‡b ivL‡Z n‡e, †h‡nZz Av‡jvi cÖwZmiY Av‡jvi e‡Y©i Dci wbf©ikxj †m‡nZz wbw`©ó gva¨‡g µvwšÍ †KvY ev msKU

†Kv‡Yi gvb Av‡jvi e‡Y©i Dci wbf©ikxj| A_©vr Av‡jvi wewfbœ e‡Y©i Rb¨ µvwšÍ †KvY ev msKU †Kv‡Yi gvbI

wewfbœ n‡e| †hgb njy` Av‡jvi Rb¨ cvwbi mv‡c‡¶ Kv‡Pi µvwšÍ †KvY 60°| wKš‘ jvj Av‡jvi Rb¨ 59° Avevi

†e¸wb Av‡jvi Rb¨ cÖvq 61°|

c~Y© Af¨šÍixY cÖwZdj‡bi kZ©

1) Av‡jvK iwk¥ Nb gva¨g †_‡K nvjKv gva¨‡g †h‡Z n‡e|

2) AvcZb †KvY msKU †Kv‡Yi †_‡K eo n‡Z n‡e|

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 222

10.2.2 gixwPKv t c~Y© Af¨šÍixY cÖwZdj‡bi D`vniY

( Mirage : Example of Total Internal Reflection and Mirage) c~Y© Af¨šÍixY cÖwZdj‡bi Kvi‡Y giæf~wg‡Z m„ó gixwPKv AwZ cwiwPZ D`vniY| DËß giæf~wg‡Z giæPvix cw_K

cÖvqk gixwPKv †`L‡Z cvb Ges weåvšÍ nb| gixwPKv nj GK ai‡Yi `„wó åg| giæf~wgi evjyKvgq a~a~ cÖvšÍ‡i

LiZv‡c wK¬ó cw_K Zv‡`i mvg‡b ¯í `~‡i cvwbc~Y© giæ`¨v‡bi `„k¨ †`L‡Z cvb| cvwb I Qvqvi Avkvq Zviv

†mw`‡K avweZ nb| wKš‘ wbw`©ó ¯’v‡b †h‡q †`‡Lb †mLv‡b †Kvb giæ`¨vb bvB eis AviI `~‡i giæ`¨vb m‡i †M‡Q|

Gfv‡e cw_K GwM‡q hvb| wKš‘ cw_K †Kvb giæ`¨vb †Zv cvbB bv eis AwaK K¬všÍ n‡q A‡b‡K g„Zz¨i †Kv‡j X‡j

c‡ob|

ZvB G‡K ejv nq gvqv gixwPKv| Avm‡j gixwPKv GK ai‡Yi Av‡jvKxq NUbv hv Av‡jvi Af¨šÍixY cÖwZdj‡bi

Kvi‡Y msNwUZ nq|

gixwPKvi e¨vL¨v t cÖPÛ m~h© Zv‡c giæf~wgi evjy Lye ZvovZvwo Mig nq| d‡j evjy msjMœ evZvmI Lye Mig nq|

G‡Z evjy msjMœ ¯Í‡ii evqy Lye nvjKv nq| f~-c„ô †_‡K hZ Dc‡i IVv hvq evhy ͇ii ZvcgvÎv ZZ Kg nq| ZvB

f~ msjMœ evqy ¯Íi †_‡K hZB Ic‡i IVv hvq evqy ¯Íi ZZ Nb nq| GAe¯’vq giæf~wg‡Z `~‡i †Kvb †LRyi MvQ Q

†_‡K cw_‡Ki †Pv‡L Avmv Av‡jvK iwk¥ av‡c av‡c NbZi gva¨g †_‡K jNyZi gva¨‡g cÖ‡ek Ki‡Z _v‡K, d‡j

cÖwZmwiZ iwk¥ Awfj¯ †_‡K µgk `~‡i m‡i †h‡Z _v‡K| Gfv‡e euvK‡Z euvK‡Z Ggb †Kvb ͇i †cŠuQvq †hLv‡b

AvcZb †KvY µvwšÍ †Kv‡Yi †P‡q eo nq| d‡j AvcwZZ Av‡jvK iwk¥i cÖwZmiY bv n‡q c~Y© Af¨šÍixY cÖwZdjb

nq|

wPÎ t 10.4 giæf~wg‡Z gixwPKv (ev‡g) Ges cÖwZwe¤ MV‡bi iwk¥ wPÎ ( Wv‡b)

cÖwZdwjZ iwk¥ nvjKv gva¨g †_‡K Nb gva¨‡g wd‡i Av‡m| Ges cÖwZ ¯Í‡i µgk Awfj‡¤i w`‡K †eu‡K Av‡m|

Gfv‡e GK mgq `k©‡Ki (cw_‡Ki) †Pv‡L cÖ‡ek K‡i| GB iwk¥‡K †cQ‡b evov‡j g‡b nq iwk¥¸‡jv Q′ we›`y †_‡K

Avm‡Q| d‡j Q′ Ae¯’v‡b †LRyi Mv‡Qi D‡ëv cÖwZwe¤ †`Lv hvq (wPÎ- 10.4)| Dciš‘ ZvcgvÎvi wbqZ cwieZ©‡bi

Kvi‡Y evqy ¯Í‡ii NbZ¡ AweiZ cwiewZ©Z n‡Z _v‡K| d‡j Mv‡Qi cÖwZwe¤wUi Ae¯’vb wbqZ cwiewZ©Z n‡Z _v‡K,

g‡b nq cÖwZwe¤wU Kuvc‡Q| Rjvk‡qi cv‡o †Kvb Mv‡Qi cvwb‡Z cov cÖwZwe¤^wU †hgb Kuvc‡Z _v‡K, wVK †Zgwb

g‡b nq|

cw_‡Ki †Pv‡L GB NUbv aiv c‡o bv| wZwb Mv‡Qi D‡ëv cÖwZwe¤^ Ges Zv Kuvc‡Z †`‡L Rjvkq e‡j weåvšÍ nb|

Gfv‡eB gwiwPKv m„wó nq|

Avcwb hw` ˆPÎ ˆekv‡Li Suv-Suv `ycy‡i duvKv gv‡Vi g‡a¨ `uvwo‡q A_ev PjšÍ ev‡m e‡m `~‡ii MvQ cvjvi w`‡K

ZvKvb, g‡b n‡e MvQ cvjvi mvwii mvg‡b †Kvb wekvj Rjvkq ev wej| Ges we‡ji cvwb‡Z MvQcvjv¸‡jvi D‡ëv

cÖwZwe¤^ co‡Q| cÖwZwe¤^ ‡jv Kuvc‡Q e‡jI g‡b n‡e|

10.2.3 AcwUK¨vj dvBevi I Zvi e¨envi (Optical Fibre and It’s Use) AcwUK¨vj dvBevi ev Av‡jvK Zš‘ GK ai‡Yi miæ (cÖvq Pz‡ji g‡Zv) ¯^”Q Zš‘ we‡kl| GwU ˆZwi nq mvaviYZ

KvP w`‡q| Kv‡Pi ˆZwi n‡jI GwU AZ¨šÍ bgbxq Ges ejv evûj¨ wb‡iU| mvaviY Kv‡Pi †_‡K Gi cÖwZmiYv¼

†ek †ewk cÖvq 1.7| GK cÖv‡šÍ Av‡jv AvcwZZ n‡j Gi †`qv‡j c~Y© Af¨šÍixY cÖwZdjb cÖwµqvq Av‡jv µgk

c`v_©weÁvb

BDwbU 10 c„ôv # 223

GwM‡q hvq Ges Zš‘i Ab¨ cÖvšÍ w`‡q wbM©Z nq| evB‡ii evqy gva¨g †_‡K †fZ‡ii Zš‘-gva¨‡gi cÖwZmiYv¼ †ek

†ewk nIqvq Af¨šÍixY cÖwZdjb mnR nq| Gi evB‡i GK ai‡Yi Av‡jvK cÖwZdjK c`v‡_©i AveiY †`qv _v‡K

hv‡K e‡j K¬vwWs (wPÎ 10.5)| d‡j Av‡jvi †Kvb iwk¥ cÖwZmwiZ n‡jI cybivq Zš‘i g‡a¨ wd‡i Av‡m| d‡j GK

cÖvšÍ w`‡q Av‡jvK kw³ XzwK‡q w`‡j Ab¨ cÖvšÍ w`‡q m¤ú~Y© Av‡jv †ewi‡q Av‡m ( wPÎ 10.6)| Zš‘ hZB `xN© ev

AvuKv euvKv ev †cuPv‡bv †nvK Gi g‡a¨ Av‡jvi MwZ e¨nZ nq bv| Dciš‘‘ AvenvIqv I †QvU LvU AvNvZ †_‡K

iÿvi Rb¨ Gi evB‡i bgbxq wKš‘ †UKmB c`v‡_©i AveviY †`qv _v‡K|

wPÎ t 10.5 AcwUKvj dvBev‡ii KvVv‡gv

wPÎ t 10.6 AcwUKvj dvBevi †hfv‡e KvR K‡i

AcwUK¨vj dvBev‡ii e¨envi

†Uwj‡hvMv‡hv‡Mi †ÿ‡Î t A‡bK¸‡jv AcwUK¨vj Zš‘ GKmv‡_ K‡i evwÛj K‡i ˆZwi Kiv nq AcwUK¨vj †Kej|

Ges Gi ga¨ w`‡q A‡bK `~‡i `~‡i Av‡jvK ms‡KZ cvVvb nq| B`vwbs †Uwj‡hvMv‡hv‡Mi †ÿ‡Î Gi eûj e¨envi

†`Lv hvq| AcwUK¨vj dvBevi w`‡q j¤v `~i‡Z¡ A‡bK Kg mg‡q wecyj cwigvY Z_¨ cwienY Kiv hvq| Gi myweavi

g‡a¨ D‡jøL‡hvM¨ n‡jv, Gi gva¨‡g Z_¨ cwien‡b Z_¨ ÿq Kg nq, ZvwoZ‡PŠ¤Kxq cÖfve gy³, LiP Kg | GKwU

Zvgv ev avZe Zv‡ii ga¨ w`‡q GKev‡i GKwU gvÎ Zwor ms‡KZ cvVvb hvq Ges AwaK `~i‡Z¡ †h‡Z ‡h‡Z

ms‡KZwU `ye©j n‡q GKmgq nvwi‡q hvq| AcwUK¨vj dvBev‡ii ga¨ w`‡q GKev‡i GKmv‡_ 10 nvRvi Av‡jvK

ms‡KZ †cÖiY Kiv hvq| Dciš‘ G‡ÿ‡Î †Kvb kw³i AcPq bv nIqvq ms‡KZwU hZ `~i‡Z¡B hvK bv ‡Kb `~e©j nq

bv| avZe ms‡hvM jvB‡b ˆe`y¨wZK ¯úvK© n‡q Av¸b aivi fq _v‡K| dvBevi †Ke‡j Av¸b aivi †Kvb AvksKv

m¤¢vebv bvB|

wPwKrmv †ÿ‡Î t wPwKrmv †ÿ‡ÎI AcwUK¨vj dvBev‡ii e¨envi †ek myweavRbK| †h‡nZz GB Zš‘‡K AZ¨šÍÍ miæ,

bgbxq I cvZjv Kiv hvq, ZvB mn‡RB i‡³i agbx, dzmdzm Ges †`n Af¨šÍ‡ii wewfbœ duvcv As‡k cÖ‡ek Kiv‡bv

hvq| d‡j wPwKrmK Acv‡ikb QvovB †`‡ni †fZ‡ii Ask¸‡jv ev „k¨vejx †`L‡Z cv‡ib|

†hgb cvK¯’jxi †fZ‡ii Ae¯’v †`Lvi Rb¨ GKwU miæ AcwUK¨vj wUDe Mjvi ga¨w`‡q cvK¯’jx ch©šÍ †cŠu‡Q †`qv

nq| bjwU g~jZ GK¸”Q Zš‘i GKwU mym½Z evwÛj| K‡qKwU Zš‘ w`‡q Av‡jv cvwV‡q cvK¯’jxi †fZi Av‡jvwKZ

Kiv nq| Ab¨ Zš‘ w`‡q Av‡jv wd‡i G‡m K¨v‡givi †j‡Ý c‡o| evB‡i †_‡K †`Lv ev Qwe †Zvjv hvq| Gfv‡e Qwe

†Zvjvi c×wZwUi bvg G‡Ûv‡¯‹vwc|

Ab¨vb¨ e¨envi t B`vwbs Uvb, Pvc, ZvcgvÎv BZ¨vw`i DcvË msMÖ‡ni gva¨g (ev †mÝi) wnmv‡e AcwUK¨vj dvBevi

e¨envi Kiv n‡”Q| Gme h‡š¿i bvg dvBevi AcwUK †mÝi| Av‡M †mÝi Kv‡R Zwor hš¿ e¨envi n‡Zv| G‡Z yN©Ubvi AvksKv Ges

LiP `yBB †ewk wQj| †Zj wk‡í e¨eüZ †m‡mwgK nvB‡Wªv‡dvb ˆZwi‡Z,

†jRvi gvB‡µv‡dvb ˆZwi‡Z AcwUK¨vj dvBevi e¨envi n‡”Q| †evwqs 767

Gi AcwUK¨vj MvB‡iv‡¯‹v‡c, GgbwK Mvwoi †`nvsk ˆZwi‡ZI AvRKvj

AcwUK¨vj dvBevi e¨eüZ n‡”Q|

wPÎ t 10. 7 Av‡jvK m¾vq

AcwUK¨vj dvBevi

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 224

nvjKv A_P gReyZ Ges †UKmB e‡j myU‡Km, weªd‡Km, †Pqvi AvmevecÎ, hvbevn‡bi †`nvsk ˆZwi‡ZI

dvBevi Møvm e¨eüZ nq nq|

Av‡jvK m¾vq AcwUK¨vj dvBev‡ii e¨enviI D‡jøL‡hvM¨fv‡e jÿ¨Yxq (wPÎ 10.7)| AcwUK¨vj dvBevi ev

Av‡jvK Zš‘ c`v_©weÁv‡bi GK we¯§qKi Avwe®‹vi|

mvi-ms‡ÿc:

µvwšÍ †KvY : wbw`©ó e‡Y©i Av‡jvK iwk¥ Nb gva¨g †_‡K nvjKv gva¨‡g cÖwZmwiZ nIqvi mgq AvcZb †Kv‡Yi †h

gv‡bi Rb¨ cÖwZmiY †KvY 90° A_©vr GK mg‡KvY nq A_©vr cÖwZmwiZ iwk¥ we‡f`Zj †N‡l hvq, Zv‡K H nvjKv

gva¨‡gi mv‡c‡¶ mswkøó Nb gva¨‡gi msKU †KvY ev µvwšÍ †KvY e‡j|

c~Y© Af¨šÍixY cÖwZdjb : wbw`©ó e‡Y©i Av‡jvK iwk¥ Nb gva¨g †_‡K nvjKv gva¨‡g µvwšÍ †Kv‡Yi †P‡q eo gv‡bi

†Kv‡Y AvcwZZ n‡j Av‡jvK iwk¥ cÖwZmwiZ bv n‡q `yB gva¨‡gi we‡f` Zj †_‡K cÖwZdj‡bi wbqg Abymv‡i

m¤ú~Y©iƒ‡c Nb gva¨‡gi Af¨šÍ‡i (Av‡Mi gva¨‡g) wd‡i Av‡m Ges cÖwZdj‡bi wbqg †g‡b P‡j| Av‡Mi gva¨‡g

wd‡i Avmvi GB cÖwµqv‡K Af¨šÍixY cÖwZdjb e‡j|

[ [ ]gixwPKv : GK ai‡Yi Av‡jvKxq NUbv hv Av‡jvi Af¨šÍixY cÖwZdj‡bi Kvi‡Y msNwUZ nq|

cv‡VvËi g~j¨vqb -10.2

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1 †Kvb gva¨‡gi µvwšÍ †KvY 24° ? (K) cvwb ‡_‡K nxi‡Ki (L) nxiK †_‡K evqyi

(M) KvP †_‡K nxi‡Ki (N) nxiK †_‡K cvwbi

2 †Kvb †Kvb †¶‡Î Av‡jvi c~Y© Af¨šÍixY cÖwZdjb NU‡e? hLb -

(K) i > θc (L) i < θc

(M) i = θc (N) i = 90° 3 †Uwj‡dv‡bi jvB‡b †KvbwU e¨envi myweav RbK?

(K) AcwUK¨vj dvBevi (L) Zvgvi Zvi

(M) avZe Zvi (N) L I M

cvV-3 †jÝ (Lens)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. †jÝ I †j‡Ýi cÖKvi‡f` e¨vL¨v Ki‡Z cvi‡eb|

2. †jÝ msµvšÍ K‡qKwU c` I ivwki msÁvmn e¨vL¨v Ki‡Z Ges wPÎ wb‡`©k Ki‡Z cvi‡eb|

3. †j‡Ýi mvnv‡h¨ cÖwZwe¤ MV‡bi e¨L¨v`v‡bi Rb¨ cÖ‡qvRbxq iwk¥ wPÎ AuvK‡Z cvi‡eb|

10.3.1 †jÝ (Lens) `ywU †MvjKxq A_ev GKwU †MvjKxq Ges GKwU mgZj c„ô Øviv Ave× †Kvb ¯^”Q cÖwZmviK Av‡jvK

gva¨g‡K †jÝ e‡j| mvaviYZ †jÝ Kv‡Pi ˆZwi nq| Z‡e we‡kl we‡kl †¶‡Î cøvw÷K, †KvqvU©R Ggb

Kx Zij c`v_© ev Aa©Zij c`v_© w`‡qI †jÝ ˆZwi n‡Z cv‡i| †jÝ cÖavbZ `yB cÖKvi,- Awfmvix †jÝ

ev DËj †jÝ Ges Acmvix †jÝ ev AeZj †jÝ|

c`v_©weÁvb

BDwbU 10 c„ôv # 225

Awfmvix ev DËj †jÝ (Convex Lens) : †h †j‡Ýi ga¨ w`‡q GK ¸”Q Av‡jvK iwk¥ cÖwZmwiZ n‡q

cÖwZmi‡Yi ci GKwU wbw`©ó we›`y‡Z wgwjZ nq Zv‡K Awfmvix

†jÝ e‡j| MVb Abymv‡i GB †j‡Ýi ga¨ fvM DuPz ev †gvUv

Ges cÖvšÍ fvM miæ, ZvB G‡K ¯’~j ga¨ ev DËj †jÝI e‡j

(wPÎ 10.8)|

wPÎ 10.8 Awfmvix †j‡Ýi ga¨w`‡q Av‡jvi

cÖwZmiY

Acmvix ev AeZj †jÝ (Concave Lens) : †h †j‡Ýi ga¨ w`‡q GK ¸”Q Av‡jvK iwk¥ cÖwZmwiZ n‡q

cÖwZmi‡Yi ci Pvwiw`‡K Qwo‡q c‡o Zv‡K Acmvix †jÝ

e‡j| MVb Abymv‡i GB †j‡Ýi ga¨fvM miæ ev cvZjv Ges

cÖvšÍ fvM †gvUv ZvB G‡K ¶xY ga¨ ev AeZj †jÝI e‡j (wPÎ

10.9)| wPÎ 10.9 Acmvix †j‡Ýi ga¨w`‡q Av‡jvi

cÖwZmiY

Z‡ji AvK…wZi Dci wfwË K‡i DËj (Awfmvix) Ges AeZj (Acmvix) cÖ‡Z¨K cÖKvi †j݇K Avevi wZb fv‡M

fvM Kiv nq h_v-

DËj †jÝ : wØ-DËj †jÝ, mgZ‡jvËj †jÝ, AeZ‡jvËj †jÝ

AeZj †jÝ : wØ-AeZj †jÝ, mgZjveZj †jÝ, DËjveZj †jÝ

Zvn‡j †j‡Ýi cÖKvi †f` g~jZ QqwU|

1. wØ-DËj †jÝ (Bi-convex lens) : †h †j‡Ýi `yB ZjB DËj Zv‡K wØ-DËj ev D‡fvËj †jÝ e‡j| [ wPÎ 10.10

(K)]

2. mgZ‡jvËj †jÝ (Plno-convex lens) : †h †j‡Ýi GKwU Zj mgZj Ges GKwU Zj DËj Zv‡K mgZ‡jvËj

†jÝ e‡j| [ wPÎ 10.10 (L)]

3. AeZ‡jvËj †jÝ (Cocavo-convex lens): †h †j‡Ýi GKwU Zj AeZj Ges Aci GKwU Zj DËj Zv‡K

AeZ‡jvËj †jÝ e‡j| [ wPÎ 10.10 (M)]

wPÎ t 10.10 wewfbœ cÖKvi DËj †jÝ

wPÎ t 10.11 wewfbœ cÖKvi AeZj †jÝ

4. wØ-AeZj †jÝ (Bi-concave lens) : †h †j‡Ýi `yB ZjB AeZj Zv‡K wØ-AeZj ev D‡fveZj †jÝ e‡j|

[ wPÎ 10.11 (K)]

5. mgZjveZj †jÝ (Plno-concave lens): †h †j‡Ýi GKwU Zj mgZj Ges GKwU Zj AeZj Zv‡K

mgZjveZj †jÝ e‡j| [ wPÎ 10.11 (L)]

6. DËjveZj †jÝ (Convexo-concave lens) : †h AeZj †j‡Ýi GKwU Zj DËj Ges Aci GKwU Zj AeZj

Zv‡K DËjveZj †jÝ e‡j| [ wPÎ 10.11 (M)]

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 226

AeZ‡jvËj Ges DËjveZj †j‡Ýi g‡a¨ AvcvZ `„wó‡Z †Kvb cv_©K¨ bvB g‡b nq| wKš‘ Av‡jvK iwk¥ †h Z‡j

AvcwZZ nq †mB Zj‡K Av‡M we‡ePbv Ki‡j cÖZxqgvb n‡e cÖ_gwU Awfmvix Ges wØZxqwU Acmvix ‡jÝ|

10.3.2 K‡qKwU cÖ‡qvRbxq msÁv (A Few important definitions) : †j‡Ýi ga¨ w`‡q cÖwZmi‡Yi wbqg Abymv‡i Av‡jvK iwk¥ cÖwZmwiZ nq| d‡j j¶¨e¯‘i cÖwZwe¤ MwVZ nq| Gme

cÖwZwe‡¤^i Ae¯’vb, ˆewkó¨ eyS‡Z Ges †j‡Ýi ga¨ w`‡q cÖwZmwiZ Av‡jvK iwk¥i †iLv wPÎ AuvK‡Z K‡qKwU

¸iæZ¡c~Y© c‡`i m‡½ cwiwPZ nIqv cÖ‡qvRb| †m¸‡jv wb‡gœ D‡jøL Kiv n‡jv|

1. cÖavb A¶ (Principal axis) : †h ywU †MvjK c„ô Øviv †jÝwU MwVZ Zv‡`i Df‡qi eµZvi †K‡› ªi ga¨ w`‡q

MgbKvix mij‡iLv‡K †j‡Ýi cÖavb A¶ e‡j|

wPÎ t 10.12 (K) DËj †j‡Ýi cÖavb A¶

wPÎ t 10.12 (L) AeZj †j‡Ýi cÖavb A¶

10.12 (K) wP‡Î GKwU DËj †j‡Ýi Ges 10.12 (L) wP‡Î GKwU AeZj †jÝi MVb I cÖavb Zj †`Lvb n‡q‡Q|

†jÝ `ywU †h †MvjK Øviv MwVZ Zv‡`i †K›`ª C I C1 †`Lvb n‡q‡Q| cÖ‡Z¨K wP‡Î C C1 mij‡iLvwU †j‡Ýi cÖavb

A¶| †j‡Ýi GKwU c„ô mgZj n‡j †Mvjxq c„‡ôi eµZvi †K›`ª †_‡K mgZ‡ji Dci Aw¼Z Awfj¤wU n‡e cÖavb

A¶|

2. Av‡jvK †K›`ª (Optical centre) : †j‡Ýi GK c„‡ô

AvcwZZ Av‡jvK iwk¥ Ab¨ c„ô w`‡q wbM©Z nIqvi mgq hw`

AvcwZZ iwk¥i mgvšÍivj fv‡e wbM©Z nq ev w`K cwieZ©b bv

K‡i Zv n‡j H iwk¥ †j‡Ýi cÖavb A‡¶i †h we›`y w`‡q hvq

ev †h we›`y‡Z †Q` K‡i Zv‡K H †j‡Ýi Av‡jvK †K›`ª e‡j|

10.13 wP‡Î DËj I AeZj Dfj †j‡Ýi Av‡jvK †K›`ª

O|

wPÎ t 10.13 †j‡Ýi Av‡jvK †K› ª

3. cÖavb †dvKvm (Principal focus) : †j‡Ýi Dci AvcwZZ cÖavb A‡¶i mgvšÍivj Ges wbKUeZx© iwk¥¸”Q

cªwZmi‡Yi ci cÖavb A‡¶i Dci †h we›`y‡Z wgwjZ nq (DËj †j‡Ý) A_ev †h we›`y †_‡K Qwo‡q co‡Q e‡j g‡b

nq (AeZj †j‡Ý), †mB we›`y‡K H †j‡Ýi cÖavb †dvKvm e‡j|

wPÎ 10.14 (K) DËj †j‡Ýi cÖavb †dvKvm

wPÎ 10.14 (L) AeZj †j‡Ýi cÖavb †dvKvm

10.14 (K) wP‡Î GKwU DËj †j‡Ýi Dci AvcwZZ Av‡jvK iwk¥ cÖwZmi‡Yi ci cÖavb A¶ CO Gi Dci F

we›`y‡Z wgwjZ n‡q‡Q| F we› ywU †jÝwUi cÖavb †dvKvm ev ms‡¶‡c †dvKvm we› y&|

10.14 (L) wP‡Î GKwU AeZj †j‡Ýi Dci AvcwZZ Av‡jvK iwk¥ cÖwZmi‡Yi ci Pvwiw`‡K Qwo‡q co‡Q wKš‘

(†cQb w`‡K ewa©Z Ki‡j) g‡b n‡”Q cÖavb A¶ OC Gi Dci F we› y †_‡K cÖwZm„Z n‡”Q ev Qwo‡q co‡Q| F

c`v_©weÁvb

BDwbU 10 c„ôv # 227

we›`ywU †jÝwUi cÖavb †dvKvm ev ms‡¶‡c †dvKvm we›`y&| j¶¨ Kiæb DËj †j‡Ýi cÖavb †dvKvm GKwU m` we›`y

Ges AeZj †j‡Ýi cÖavb †dvKvm GKwU Am` we›`y|

Av‡jvK iwk¥ †j‡Ýi †h †Kv‡bv GK c„‡ô AvcwZZ n‡q Aci c„ô w`‡q wbM©Z n‡Z cv‡i ZvB cÖ‡Z¨K †j‡ÝiB

Av‡jvK †K‡› ªi `yÕw`‡K ywU cÖavb †dvKvm _v‡K|

4. †dvKvm `~iZ¡ (Focal length) : Av‡jvK †K›`ª †_‡K cÖavb †dvKvm we›`y ch©šÍ `~iZ¡‡K †j‡Ýi †dvKvm `~iZ¡

e‡j| 10.14 wP‡Î OF †dvKvm ~iZ¡| †dvKvm ~iZ¡‡K f Øviv cÖKvk Kiv nq|

4. †dvKvm Zj (Focal plane) : †Kv‡bv †j‡Ýi cÖavb

†dvKv‡mi ga¨ w`‡q cÖavb A‡¶i mv‡_ j¤fv‡e †h

mgZj Kíbv Kiv hvq Zv‡K †dvKvm Zj e‡j|

10.15 wP‡Î PQ ZjwU cÖavb †dvKv‡mi ga¨w`‡q

cÖavb A‡ÿi Dci j¤fv‡e KwíZ †dvKvm Zj|

†`Lv hv‡”Q cÖavb †dvKvm †MŠY †dvKvm GB Z‡j

Aew¯’Z|

wPÎ 10.15 †dvKvm Zj

10.3.3 †j‡Ýi iwk¥ wPÎ (Ray Diagram for Lens) DËj ev AeZj †j‡Ýi mvg‡b †Kv‡bv e¯‘ ivL‡j †j‡Ýi ga¨ w`‡q Av‡jvi cÖwZmi‡Yi Rb¨ cÖwZwe¤ MwVZ nq| GB

we‡¤i Ae¯’vb, AvKvi I cÖK…wZ Rvb‡Z n‡j iwk¥ wPÎ AvuK‡Z nq| iwk¥ wP‡Îi gva¨‡g e¯‘ †_‡K wbtm„Z ev wbM©Z

iwk¥¸”Q †j‡Ý cÖwZmi‡Yi ci †Kv_vq wgwjZ nq ev †Kv_v †_‡K wbm„Z n‡”Q e‡j g‡b nq Zv Rvbv hvq| †j‡Ýi

cÖavb A¶, cÖavb †dvKvm, Av‡jvK †K›`ª wbw`©ó, ZvB K‡qKwU we‡kl AvcwZZ iwk¥ cÖwZmwiZ n‡q †Kvb c‡_ hv‡e

Zv R¨vwgwZK wPÎ Gu‡K mn‡R w¯’i Kiv hvq| GB mg¯Í iwk¥i Mgb c_ ev iwk¥ wPÎ †_‡K we‡¤i Ae¯’vb, AvK…wZ

Ges cÖK…wZ wbY©q Kiv hvq| G Rb¨ DËj Ges AeZj Dfq cÖKvi †j‡Ýi †¶‡Î mPivPi wb‡Pi wZb ai‡Yi iwk¥

we‡ePbv Kiv nq|

1. †j‡Ýi Av‡jvK †K› ª w`‡q AvcwZZ iwk¥

2. †j‡Ýi cÖavb A‡¶i mv‡_ mgvšÍivj fv‡e AvcwZZ iwk¥

3. †j‡Ýi cÖavb †dvKv‡mi ga¨ w`‡q ev cÖavb †dvKvm eivei AvcwZZ iwk¥

†j‡Ýi ga¨ w`‡q Av‡jvK iwk¥ `yÕevi cÖwZmwiZ nq| cÖ_g evi evqy gva¨g †_‡K KvP (†j‡Ýi Dcv`vb) gva¨‡g;

wØZxq evi KvP gva¨g †_‡K evqy gva¨‡g| wKš‘ wPθ‡jv mnR Kivi Rb¨ †j‡Ýi ga¨fvM w`‡q cÖavb A‡¶i Dci

GKwU Dj¤ †iLv eivei Av‡jvK iwk¥i GKevi w`K cwieZ©b †`Lvb nq|

1. †j‡Ýi Av‡jvK †K› ª w`‡q AvcwZZ iwk¥ cÖwZmi‡Yi ci †mvRvmywR hvq|

wPÎ t 10.16 (K)

wPÎ t 10.16 (L)

10.16 (K) I (L) wP‡Î h_vµ‡g DËj I AeZj †j‡Ý GKwU iwk¥ AO †j‡Ýi Av‡jvK †K›`ª O eivei AvcwZZ

n‡q‡Q, GwU w`K cwieZ©b bv K‡i †mvRvmywR OB c‡_ cÖwZmwiZ n‡q‡Q|

2. †j‡Ýi cÖavb A‡¶i mv‡_ mgvšÍivj fv‡e AvcwZZ iwk¥ cÖwZmi‡Yi ci cÖavb †dvKvm w`‡q hvq (DËj †j‡Ý)

A_ev cÖavb †dvKvm †_‡K Avm‡Q e‡j g‡b nq (AeZj †j‡Ý)|

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 228

wPÎ t 10.17 (K)

wPÎ t 10.17 (L)

10.17 (K) wP‡Î GKwU iwk¥ AL DËj †j‡Ýi cÖavb A¶ FOF′ Gi mgv¯Íivj fv‡e L we›`y‡Z AvcwZZ n‡q cÖavb

†dvKvm F w`‡q LFB c‡_ cÖwZmwiZ nq| 10.17 (L) wP‡Î AeZj †j‡Ýi cÖavb A¶ FOF′ Gi mgvšÍivj GKwU

iwk¥ AL, L we›`y‡Z AvcwZZ n‡q LB c‡_ Ggb fv‡e cÖwZmwiZ nq †hb GwU cÖavb †dvKvm F we›`y †_‡K Avm‡Q

e‡j g‡b nq| G‡¶‡Î LB †K †cQ‡b ewa©Z Ki‡j cÖavb A‡¶i mv‡_ F we› y‡Z wgwjZ n‡e|

3. †j‡Ýi cÖavb †dvKv‡mi ga¨ w`‡q (DËj †j‡Ý) ev cÖavb †dvKvm eivei (AeZj †j‡Ý) AvcwZZ iwk¥

cÖwZmi‡Yi ci cÖavb A‡¶i mgvšÍivj n‡q hvq|

10.18 (K) wP‡Î GKwU iwk¥ AL DËj †j‡Ýi cÖavb †dvKvm eivei (ga¨ w`‡q) †j‡Ýi Dci L we›`y‡Z AvcwZZ

n‡q cÖavb A¶ FOF′ Gi mgvšÍivj n‡q LB c‡_ cÖwZmwiZ nq|

wPÎ t 10.18 (K)

wPÎ t 10.18 (L)

10.18 (L) wP‡Î AeZj †j‡Ýi cÖavb †dvKvm F Awfgy‡L GKwU iwk¥ AL †j‡Ýi L we›`y‡Z AvcwZZ n‡q cÖavb

A¶ FOF′ Gi mgvšÍivj n‡q LB c‡_ cÖwZmwiZ nq|

mvi-ms‡ÿc:

†jÝ t ywU †MvjKxq A_ev GKwU †MvjKxq Ges GKwU mgZj c„ô Øviv Ave× †Kvb ¯”Q cÖwZmviK Av‡jvK

gva¨g‡K †jÝ e‡j|

Awfmvix ev DËj †jÝ t †h †j‡Ýi ga¨ w`‡q GK ¸”Q Av‡jvK iwk¥ cÖwZmwiZ n‡q cÖwZmi‡Yi ci GKwU

wbw ©ó we› y‡Z wgwjZ nq Zv‡K Awfmvix †jÝ e‡j|

Acmvix ev AeZj †jÝ t †h †j‡Ýi ga¨ w`‡q GK ¸”Q Av‡jvK iwk¥ cÖwZmwiZ n‡q cÖwZmi‡Yi ci

Pvwiw`‡K Qwo‡q c‡o Zv‡K Acmvix †jÝ e‡j|

†jÝ Qq cÖKvi h_v- wØ-DËj, mgZ‡jvËj, AeZ‡jvËj, AeZj, wØ-AeZj, mgZjveZj Ges DËjveZj

†jÝ|

†dvKvm ~iZ¡ t Av‡jvK †K› ª †_‡K cÖavb †dvKvm we› y ch©šÍ ~iZ¡‡K †j‡Ýi †dvKvm ~iZ¡ ev †dvKvm

ˆ`N©¨ e‡j|

c`v_©weÁvb

BDwbU 10 c„ôv # 229

cv‡VvËi g~j¨vqb -10.3

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| †j‡Ýi ga¨ w`‡q MgbKvix Av‡jvK iwk¥ KZevi cÖwZmwiZ nq?

(K) GK (L) `yB

(M) wZb (N) Pvi

2| †h †j‡Ýi ga¨fvM cyiæ Ges cÖvšÍ fvM miæ †mwU †Kvb †kÖYxi †jÝ?

(K) Awfmvix (L) Acmvix

(M) mgZ‡jvËj (N) mg AeZj

3| Awfmvix †j݇K Kx ejv nq?

(K) AeZj †jÝ (L) ¶xY ga¨ †jÝ

(M) Acmvix †jÝ (N) DËj †jÝ

cvV- 4 †j‡Ý cÖwZwe¤ (Image by Lens)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. DËj †j‡Ý e¯‘i ev¯Íe ev m` cÖwZwe¤ m„wó e¨vL¨v Ki‡Z cvi‡eb|

2. DËj †j‡Ý e¯‘i Aev¯Íe cÖwZwe¤ m„wó e¨vL¨v Ki‡Z cvi‡eb|

3. AeZj †j‡Ý e¯‘i cÖwZwe¤ m„wó e¨vL¨v Ki‡Z cvi‡eb|

4. cÖwZmi‡Yi d‡j wKfv‡e cÖwZwe‡¤i m„wó nq, iwk¥ wP‡Îi mvnv‡h¨ Gu‡K †`Lv‡Z cvi‡eb|

10.4.1 †j‡Ýi cÖwZwe¤ m„wó (Image Formation by Lens) Avgiv Rvwb, †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK iwk¥¸”Q cÖwZdjb ev cÖwZmi‡Yi ci hw` wØZxq †Kv‡bv

we›`y‡Z wgwjZ nq ev wØZxq †Kvb we›`y †_‡K wbtm„Z n‡”Q e‡j g‡b nq, Zvn‡j H we›`y‡ZB cÖ_g we›`yi

cÖwZwe¤ MwVZ nq| †j‡Ýi ga¨ w`‡q Av‡jvK iwk¥ cÖwZmwiZ nq| ZvB †Kv‡bv †j‡Ýi mvg‡b e¯‘ ivL‡j

cÖwZwe¤ MwVZ nq| †j‡Ýi Øviv †Kv‡bv e¯‘i cÖwZwe¤ MV‡bi Rb¨ 10.3.3 Aby‡”Q‡` ewY©Z wbqg Abyhvqx iwk¥ wPÎ

AvuKv nq|

K. DËj †j‡Ý ev Íe cÖwZwe¤ MVb

10.20 wP‡Î LL' GKwU DËj †jÝ| C Gi Av‡jvK †K› ª, F cÖavb †dvKvm Ges F΄CF cÖavb A¶| †jÝwUi mvg‡b

cÖavb A‡¶i Ici A we›`y‡Z j¤fv‡e ’vwcZ AO GKwU we¯Í……Z j¶¨e¯‘| OA e¯‘wU AmsL¨ we›`y e¯‘i mgwó, hvi

cÖvšÍ we›`y yÕwU h_vµ‡g O (kxl©) Ges A (cv` we›`y)| GLb A Ges O we›`yi we‡¤i Ae¯’vb wbY©q Ki‡jB AO we¯Í……Z e¯‘i cÖwZwe¤ cvIqv hv‡e|

cÖ_‡g O we›`yi cÖwZwe¤ wbY©‡qi Rb¨ O we›`y †_‡K cÖavb A‡¶i mgvšÍivj OP iwk¥ AvuKv n‡jv hv cÖwZmi‡Yi ci

cÖavb †dvKvm F we›`y w`‡q hv‡e| O we›`y †_‡K Avi GKwU iwk¥ OC Av‡jvK †K›`ª C we›`yi ga¨ w`‡q OCI c‡_

cÖwZmwiZ n‡e| PF I OI cÖwZmwiZ iwk¥ `yÕwU I we›`y‡Z †Q` Ki‡e| I we› y‡Z O we› yi cÖwZwe¤ MwVZ n‡e|

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 230

A †_‡K cÖavb A¶ eivei AvcwZZ Av‡jvK iwk¥ cÖwZmi‡Yi

ci cÖavb A‡¶i Dci w`‡qB ACF c‡_ cÖwZmwiZ n‡e|

d‡j A we›`yi cÖwZwe¤ Aek¨B cÖavb A‡¶i Ici _vK‡e|

Avevi †h‡nZz AO j¶¨e¯‘wU cÖavb A‡¶i Dci j¤, †m‡nZz

cÖwZwe¤wUI cÖavb A‡¶i Dci j¤ n‡e| ZvB I †_‡K cÖavb

A‡¶i Ici IB j¤ Uvb‡j BI n‡e AO j¶¨e¯‘i cÖwZwe¤^|

wPÎ †_‡K †`Lv hvq cÖwZwe¤wU ev¯Íe ev m`, D‡ëv Ges

AvKv‡i j¶¨e¯‘ †_‡K eo|

wPÎ t 10.20 DËj †j‡Ý we¯Í……Z j¶¨e¯‘i cÖwZwe¤ MVb

L. DËj †j‡Ý Aev¯Íe cÖwZwe¤ MVb

10.21 wP‡Î LL GKwU DËj †jÝ| C-Gi Av‡jvK‡K› ª, F cÖavb

†dvKvm Ges FCF cÖavb A¶| †jÝwUi mvg‡b cÖavb A‡¶i Dci A we›`y‡Z j¤fv‡e ¯’vwcZ OA GKwU we¯Í…Z j¶¨e¯‘| OA e¯‘wU AmsL¨

we›`y e¯‘i mgwó, hvi cÖvšÍ we›`y `ywU h_vµ‡g O (kxl©) Ges A

(cv`we›`y)| GLb A Ges O we›`yi we‡¤^i Ae¯’vb wbY©q Ki‡jB AO e¯‘i cÖwZwe¤ cvIqv hv‡e|

wPÎ 10.21

O we›`y †_‡K cÖavb A‡¶i mgvšÍivj OP iwk¥ AvuKv n‡jv hv cÖwZmi‡Yi ci cÖavb †dvKvm F we›`y w`‡q hv‡e| O we›`y †_‡K Avi GKwU iwk¥ OC Av‡jvK‡K›`ª C we› yi ga¨ w`‡q OCR c‡_ cÖwZmwiZ n‡e| GB cÖwZmwiZ iwk¥Øq

Acmvix e‡j wgwjZ nq bv| G‡`i‡K wcQ‡bi w`‡K evwo‡q w`‡j I we›`y †_‡K Avm‡Q e‡j g‡b nq| myZivs I n‡”Q

O we›`yi Aev¯Íe cÖwZwe¤| GLb I †_‡K cÖavb A‡¶i Dci Aw¼Z IB j¤B n‡”Q OA j¶¨e¯‘i Aev¯Íe cÖwZwe¤

(wPÎ 10.21)|

M. AeZj †j‡Ý e ‘i cÖwZwe¤ MVb

10.22 wP‡Î LL' GKwU AeZj †jÝ| C Gi Av‡jvK †K›`ª, F cÖavb †dvKvm Ges FCF cÖavb A¶| †jÝwUi

mvg‡b cÖavb A‡¶i Ici A we›`y‡Z j¤fv‡e ¯’vwcZ AO GKwU we¯Í……Z j¶¨e¯‘| OA e¯‘wU AmsL¨ we›`y e¯‘i mgwó,

hvi cÖvšÍ we›`y `yÕwU h_vµ‡g O (kxl©) Ges A (cv` we›`y)| GLb A Ges O we›`yi we‡¤i Ae¯’vb wbY©q Ki‡jB AO we¯Í……Z e¯‘i cÖwZwe¤ cvIqv hv‡e|

O we›`y †_‡K cÖavb A‡¶i mgvšÍivj OP AvcwZZ iwk¥

Ges Gi cÖwZmwiZ iwk¥ PS AvuKv n‡jv hv cÖavb †dvKvm

F we› y †_‡K Avm‡Q e‡j g‡b n‡e| O we› y †_‡K Avi

GKwU iwk¥ OC Av‡jvK †K›`ª C we›`yi eivei AvcwZZ

n‡q OCN c‡_ cÖwZmwiZ n‡e| iwk¥ `yÕwU Acmvix|

G‡`i †cQ‡b ewa©Z Ki‡j I we›`y †_‡K Avm‡Q e‡j g‡b

n‡e| myZivs I we›`yB n‡e O we› yi cÖwZwe¤|

wPÎ 10.22 AeZj †j‡Ýi we Í……Z j¶¨e ‘i cÖwZwe¤ MVb

AO j¶¨e¯‘wU cÖavb A‡¶i Ici j¤, ZvB cÖwZwe¤wUI cÖavb A‡¶i Ici j¯ n‡e| I we›`y †_‡K cÖavb A‡¶i

Dci IB j¤ AuvKv n‡jv| IB, OA j¶¨e¯‘i cÖwZwe¤| wPÎ †_‡K †`Lv hvq cÖwZwe¤wU Aev¯Íe ev Am`&, †mvRv Ges

AvKv‡i j¶¨e¯‘ †_‡K †QvU|

10.4.2 m`& ev ev Íe I Am`& ev Aev Íe cÖwZwe¤^ (Real and Virtual Image) Avgiv Rvwb cÖwZdjb Ges cÖwZmiY Dfq †¶‡ÎB cÖwZwe¤ MwVZ nq| KLbI j¶¨e¯‘ †_‡K wb:m„Z Av‡jv

cÖwZdj‡bi ev cÖwZmi‡Yi ci wØZxq we›`y‡Z wgwjZ n‡q cÖwZwe¤ MVb K‡i, KLbI ev wØZxq we›`y †_‡K Acm„Z

n‡”Q e‡j g‡b nq| G‡¶‡ÎI cÖwZwe¤ †`Lv hvq| G me we‡¤i ˆewk‡ó¨i Dci wfwË K‡i cÖwZwe¤‡K `yB fv‡M fvM

Kiv n‡q‡Q| Av‡jvi cÖwZdjb BDwb‡U G‡`i ˆewkó¨ m¤ú‡K© we¯ÍvwiZ Av‡jvPbv n‡q‡Q| DËj †j‡Ýi †¶‡Î m` I

Am` cÖwZwe¤^ MwVZ nq wKš‘ AeZj †j‡Ý †Kej Am` cÖwZwe¤ MwVZ nq|

c`v_©weÁvb

BDwbU 10 c„ôv # 231

mvi-ms‡ÿc:

cv‡VvËi g~j¨vqb -10.4

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| j¶¨e ‘ DËj †jÝ †_‡K 2f Gi †ewk ~i‡Z¡ Aew¯’Z n‡j we‡¤i cÖK…wZ †Kgb n‡e?

(K) Am`, D‡ëv I Lwe©Z (L) m`, D‡ëv I j¶¨e ‘i mgvb

(M) m`, †mvRv I Lwe©Z (N) m`, D‡ëv I Lwe©Z

2| DËj †jÝ †_‡K 2f ~i‡Z¡ j¶¨e¯‘ _vK‡j we‡¤i Ae¯’vb †Kv_vq n‡e?

(K) f ~i‡Z¡ (L) Amxg `~i‡Z¡

(M) 2f ~i‡Z¡ (N) f I 2f Gi ga¨eZx© `~i‡Z¡

3| 15 cm †dvKvm `~i‡Z¡i GKwU DËj †j‡Ýi cÖavb A‡¶i Dci Av‡jvK †K› ª †_‡K 20 cm ~‡i ivLv e¯‘i Rb¨ m„ó cÖwZwe‡¤i ~iZ¡ v Gi †¶‡Î †KvbwU mwVK?

(K) v > 30 cm (L) v = 30 cm

(M) v < 30 cm (N) v =20 cm

cvV -5t †j‡Ýi ¶gZv I mgxKiY (Power and Equation of Lens)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. †j‡Ýi ÿgZv e¨vL¨v Ki‡Z cvi‡eb|

2. †j‡Ýi †ÿ‡Î jÿ¨e¯‘i `~iZ¡, cÖwZwe‡¤i `~iZ¡ I †dvKvm `~i‡Z¡i m¤úK© m~~PK mgxKiYwU wjL‡Z I e¨vL¨v

Ki‡Z cvi‡eb|

3. †j‡Ýi weea©b e¨vL¨v Ki‡Z cvi‡eb|

4. †j‡Ýi weea©‡bi ivwkgvjv wjL‡Z cvi‡eb|

10.5.1 †j‡Ýi ¶gZv (Power of Lens) Avgiv Rvwb DËj †jÝ cÖavb A‡¶i mgvšÍivj Av‡jvK iwk¥‡K cÖavb †dvKv‡m GKwÎZ K‡i Ges AeZj

†jÝ cÖavb A‡¶i mgvšÍivj Av‡jvK iwk¥‡K Qwo‡q †`q| GRb¨ DËj †j݇K Awfmvix Ges AeZj †j݇K

Acmvix †jÝ e‡j| wb‡P `ywU Awfmvix Ges `ywU Acmvix †jÝ †`Lv‡bv n‡q‡Q| aiv hvK cÖ‡Z¨KwU †j‡Ýi Dci

DËj †j‡Ýi mvg‡b j¶¨e¯‘i Ae¯’vb MwVZ cÖwZwe‡¤i Ae¯’vb, cÖK…wZ I AvK…wZ

2f Gi †ewk `~i‡Z¡ f I 2f Gi g‡a¨, m` I D‡ëv, Lwe©Z

2f ~i‡Z¡ 2f ~i‡Z¡ , m` I D‡ëv, j¶¨e ‘i mgvb

f I 2f Gi g‡a¨ 2f Gi †ewk `~i‡Z¡, m` I D‡ëv, weewa©Z

†dvKvm we›`y‡Z Amx‡g, m` I D‡ëv, AZ¨šÍ weewa©Z

Av‡jvK †K› ª I cªavb †dvKv‡mi g‡a¨ j¶¨e¯‘i †cQ‡b, Am` I †mvRv, weewa©Z

Amxg `~‡i †dvKvm Z‡j, m` I D‡ëv, AZ¨šÍ Lwe©Z

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 232

mgvb cwigvY mgvšÍivj Av‡jvK iwk¥ †djv n‡q‡Q| ejyb‡Zv cÖwZmi‡Yi c‡i †Kvb †j‡Ý Av‡jvi c_ †Kgb n‡e?

mwVK DËi n‡jv cÖ_g †jÝ `ywU‡Z cÖwZmwiZ Av‡jvK iwk¥‡K GKwU †dvKvm we›`y‡Z wgwjZ Ki‡e| wØZxq `ywU‡Z

g‡b n‡e GKwU †dvKvm we›`y †_‡K cÖwZmwiZ iwk¥ ¸”Q‡K Qwo‡q w`‡”Q| wb‡Pi wPθ‡jv †`Lyb|

wPÎ t 10. 23 (K)

wPÎ t 10.23 (L)

wPÎ-10.23 (K) Gi `ywU †jÝB cÖwZm„Z iwk¥‡K cÖavb †dvKv‡m GKwÎZ K‡i‡Q| wKš‘ jÿ¨ Kiæb GKUz cv_©K¨

†Pv‡L co‡Q wK? nu¨v Dc‡ii †jÝwUi †_‡K wb‡Pi †jÝwUi †dvKvm we›`y †jÝ †_‡K wbKUeZx©| Avgiv ewj

Dc‡iiwU †_‡K wb‡Pi †jÝwUi Av‡jvK iwk¥¸”Q‡K GKwÎZ Kivi ÿgZv †ewk|

GKBfv‡e wPÎ 10.23 (L) Gi `ywU †jÝB cÖwZm„Z iwk¥‡K Qwo‡q w`‡”Q| wKš‘ GKwU Ab¨wUi Zzjbvq †j‡Ýi KvQ

†_‡K| Dc‡ii †jÝwU †_‡K wb‡Pi †jÝwUi Av‡jvK iwk¥ Qwo‡q †`qvi ÿgZv †ewk| †j‡Ýi GB AwfmvwiZv Ges

AcmvwiZvi mvg_© ‡K ÿgZv ejv nq| †Kb Ggb nq? jÿ¨ Kiæb †j‡Ýi †dvKvm `~iZ¡B Gi Rb¨ `vqx| †h DËj

†jÝ iwk¥ ¸”Q‡K hZ Kv‡Q GKwÎZ K‡i Zvi †dvKvm `~iZ¡ ZZ Kg, †mB †j‡Ýi ¶gZv ZZ †ewk| Abyiƒcfv‡e †h

AeZj †jÝ iwk¥ ¸”Q‡K hZ KvQ †_‡K Qwo‡q w`‡”Q e‡j g‡b nq A_©vr hvi †dvKvm `~iZ¡ hZ Kg †mB †j‡Ýi

¶gZv ZZ †ewk| wKš‘ DËj †j‡Ýi †ejvq †dvKvmwU m`| AeZj †j‡Ýi †ejvq Am`|

†j‡Ýi Av‡jvK †K›`ª †_‡K †dvKvm we›`yi w`K Ges Av‡jvi cÖwZmiY GKB w`‡K ZvB ¶gZv aYvZ¥K| Aci w`‡K

AeZj †j‡Ýi †ejvq †dvKvmwU Am`, †j‡Ýi Av‡jvK †K›`ª †_‡K †dvKvm we›`yi w`K Av‡jvi cÖwZmi‡Yi wecixZ

w`‡K ZvB AeZj †j‡Ýi ¶gZv FYvZ¥K| †j‡Ýi †dvKvm `~iZ¡ hZ Kg nq Zvi ¶gZv ZZ †ewk nq| A_©vr

†j‡Ýi ¶gZv Zvi †dvKvm `~i‡Z¡i e¨¯ÍvbycvwZK| ev †j‡Ýi ÿgZv †K P Ges †dvKvm ˆ`N¨©K f ai‡j, P f1

|

[Ò” mgvbycv‡Zi cÖZxK wPý& | Ô P f

1Õ evK¨wU co‡Z nq P e¨¯ÍvbycvwZK f ]

†j‡Ýi ¶gZvi cÖPwjZ GKK WvBAÞvi| GK wgUvi †dvKvm ˆ`‡N© i †Kv‡bv †j‡Ýi ¶gZv‡K GK WvBAÞvi (D)

e‡j| A_©vr †j‡Ýi †dvKvm ~iZ¡ (f) wgUvi Ges ¶gZv (P) WvBAÞvi n‡j,

P = f1 ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (10.4)

wPý cÖ_v t mKj `~iZ¡ †j‡Ýi Av‡jvK †K›`ª †_‡K cwigvc Ki‡Z nq| †h mKj `~iZ¡ Av‡jvi w`‡K A_©vr

Av‡jv cÖK…Z c‡ÿ †h `~iZ¡ AwZµg K‡i Zv‡K abvZ¥K ev ev¯Íe `~iZ¡ Ges Av‡jv †h w`‡K hvq Zvi wecixZ

w`‡Ki ~iZ¡‡K FYvZ¥K ev Aev¯Íe ~iZ¡ we‡ePbv Kiv nq|

c`v_©weÁvb

BDwbU 10 c„ôv # 233

Zvrch©-1: †Kvb †j‡Ýi ¶gZv + 0.5 D ej‡Z eySvq †jÝwUi ¶gZv abvZ¥K, AZGe GwU GKwU DËj †jÝ| Ges

Gi †dvKvm `~iZ¡

1 m 2m0.5

f A_©vr cÖavb A‡¶i mgvšÍivj GK¸”Q Av‡jvK iwk¥‡K †jÝwU 2m `~‡i

GKwÎZ K‡i|

Zvrch©-2: †Kvb †j‡Ýi ¶gZv - 0.5 D ej‡Z eySvq †jÝwUi ¶gZv FYvZ¥K, AZGe GwU GKwU AeZj †jÝ|

Ges Gi †dvKvm `~iZ¡

1 m 2m-0.5

f A_©vr cÖavb A‡¶i mgvšÍivj GK¸”Q Av‡jvK iwk¥ †jÝwUi †cQ‡bi

2m `~‡ii †Kvb we›`y †_‡K Acm„Z n‡”Q e‡j g‡b n‡e|

MvwYwZK D`vniY- 10.1

GKwU †j‡Ýi †dvKvm `~iZ¡ 25cm n‡j , †jÝwUi ÿgZv KZ?

mgvavb t †dvKvm ~iZ¡, f = 25 cm = 0.25m

AZGe †jÝwUi ÿgZv,

1Pf

=

10 25m.

=4 D

10.5.2 †j‡Ýi mgxKiY (Equation of Lens) aiv hvK LL' GKwU miæ DËj †jÝ (wPÎ 10.24)| C Gi Av‡jvK †K› ª, F1 I F2 cÖ_g I wØZxq cÖavb †dvKvm

Ges F1CF2 cÖavb A¶| †jÝwUi mvg‡b cÖavb A‡¶i Ici F1 Gi evB‡i A we›`y‡Z j¤fv‡e ¯’vwcZ AO GKwU

we¯Í……Z j¶¨e¯‘|

O we›`y †_‡K cÖavb A‡ÿi mgvšÍivj OP iwk¥ wØZxq †dvKvm F2

Gi ga¨ w`‡q cÖwZm„Z nq| O †_‡K Avi GKwU iwk¥ OC

Av‡jvK †K›`ª C we›`yi ga¨ w`‡q eivei OCI c‡_ cÖwZm„Z nq|

PF2 I OI cÖwZmwiZ iwk¥ `yÕwU I we›`y‡Z †Q` Ki‡e| I we›`y‡Z O

we›`yi cÖwZwe¤ MwVZ n‡e| I †_‡K cÖavb A‡¶i Ici IB j¤

Uvb‡j BI n‡e AO j¶¨e¯‘i cÖwZwe¤|

wPÎ t 10.24

GLv‡b wPÎ 10.24 G j¶¨e ‘i ~iZ¡, CA = + u

cÖwZwe‡¤i `~iZ¡, CB = + v †dvKvm ~iZ¡, CF = + f n‡j,

f1 =

u1 +

v1 ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (10.5)

GB 10.5 bs mgxKiYwU DËj †j‡Ýi Øviv MwVZ m` we‡¤i †ÿ‡Î †j‡Ýi mgxKiY| DËj †jÝ Øviv MwVZ Am`

we¤ Ges AeZj †jÝ Øviv MwVZ we‡¤i †ÿ‡ÎI Abyiƒcfv‡e GKB mgxKiY cvIqv hvq| cieZx© †kªwYi cvV¨cy¯Í‡K

G¸‡jvi cÖwZcv`b cvIqv hv‡e| g‡b K‡i †`Lyb, beg BDwb‡Ui cvV -5 Gi 9.5.1 Aby‡”Q‡` †Mvjxq `c©‡Yi

†ÿ‡ÎI GKB mgxKiY †c‡qwQ‡jb|

AZGe (10.5) mgxKiYwU mKj cÖKvi †jÝ I †MvjKxq `c©‡Yi †ÿ‡Î MªnY‡hvM¨ mgxKiY| GwU‡K ZvB †j‡Ýi

Ges †Mvjxq `c©‡Yi mvaviY mgxKiY ejv nq|

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 234

10.5.3 weea©b I weea©‡bi ivwkgvjv (Magnification) Av‡Mi BDwb‡Ui cvV-6 G Avgiv †Mvjxq `c©‡Yi †ÿ‡Î weea©b m¤ú‡K© Av‡jvPbv K‡iwQ| mvaviY A‡_© weea©b

gv‡b KZ¸Y e„w× n‡q‡Q Zvi cwigvY| ˆeÁvwbK `„wó‡Z e„w× ev n«vm meB weea©b| g~jZ cÖwZwe‡¤i AvKvi jÿ¨e¯‘i

Zzjbvq KZ¸Y eo ev †QvU †mB ivwk‡K Zvi weea©b e‡j| GB AvKvi cwigv‡ci †ÿ‡Î we‡¤^i ˆ`N© Ges e¯‘i

ˆ`‡N© i AbycvZ‡K e¨envi Kwi| ZvB GK ejv nq ˆiwLK weea©b|

aiv hvK †Kvb j¶¨e ‘i ˆ`N© Lo Ges cÖwZwe‡¤i ˆ`N© Li| Zv n‡j,

ˆiwLK weea©b m =

i

o

LL

= ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (10.6)

m > 1 n‡j, cÖwZwe¤wU weewa©Z n‡e| A_©vr j¶¨e¯‘ †_‡K we‡¤^i AvKvi eo n‡e|

m = 1 n‡j, cÖwZwe¤wU j¶¨e¯‘i mgvb n‡e| A_©vr j¶¨e¯‘i AvKvi I we‡¤i AvKvi mgvb n‡e| m < 1 n‡j, cÖwZwe¤wU Lwe©©Z n‡e| A_©vr j¶¨e¯‘ †_‡K we‡¤^i AvKvi ‡QvU n‡e|

†jÝ DËj ev AeZj hvB †nvK, we¤ ev Íe ev Aev¯Íe Ges †mvRv ev D‡ëv hvB †nvK

weea©b n‡e,

uvm

... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (10.7)

GLv‡b, u = †j‡Ýi Av‡jvK †K› ª †_‡K jÿ¨e ‘i `~iZ¡ Ges v = †j‡Ýi Av‡jvK †K› ª †_‡K cÖwZwe‡¤i `~iZ¡|

weea©‡bi cig gvb |m| = uv ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (10.8)

mvi-ms‡ÿc:

†j‡Ýi ÿgZv : GK wgUvi †dvKvm ˆ`‡N© i †Kvb †j‡Ýi ¶gZv‡K GK WvBAÞvi (D) e‡j| A_©vr †j‡Ýi †dvKvm

`~iZ¡ (f) wgUvi Ges ¶gZv (P) WvBAÞvi n‡j,

1Pf

WvBAÞvi

†j‡Ýi ˆiwLK weea©b : †Kvb j¶¨e¯‘i ˆ`N© Lo Ges cÖwZwe‡¤i ˆ`N© Li| Zv n‡j, ˆiwLK weea©b m =

i

o

LL

A_ev, jÿ¨e ‘i `~iZ¡ = + u Ges we¤ ~iZ¡ = + v n‡j, weea©b n‡e,

uvm

m > 1 n‡j, cÖwZwe¤wU weewa©Z n‡e| A_©vr j¶¨e¯‘ †_‡K we‡¤^i“ AvKvi eo n‡e|

m = 1 n‡j, cÖwZwe¤wU j¶¨e¯‘i mgvb n‡e| A_©vr j¶¨e¯‘i AvKvi I we‡¤i AvKvi mgvb| m < 1 n‡j, cÖwZwe¤wU Lwe©©Z n‡e| A_©vr j¶¨e¯‘ †_‡K we‡¤ AvKvi ‡QvU n‡e|

cv‡VvËi g~j¨vqb -10.5

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| GKwU AeZj †j‡Ýi †dvKvm yiZ¡ 20 cm n‡j Gi ¶gZv KZ?

(K) -5 D (L) 5 D

(M) 0.5 D (N) 5m

2| †j‡Ýi ¶gZv I †dvKvm ~i‡Z¡ m¤úK© Kx?

(K) ci¤úi mgvb (L) ci¤úi mgvbycvwZK

(M) ci¤úi e¨¯ÍvbycvwZK (N) GK Ac‡ii wظY

c`v_©weÁvb

BDwbU 10 c„ôv # 235

cvV-6 : „wó I „wó ÎæwU (Vision and Defects of Vision)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. Av‡jvK iwk¥i wµqv‡iLv AsKb K‡i †Pv‡Li wµqv e¨vL¨v Ki‡Z cvi‡eb|

2. iwOb e¯‘i Av‡jvKxq Dcjwä e¨vL¨v Ki‡Z cvi‡eb|

3. †Pv‡Li Dc‡hvRb ÿgZv I ¯úó `k©‡bi by¨bZg `~iZ¡¡ ej‡Z wK eySvq Zv e¨vL¨v Ki‡Z cvi‡eb|

4. `„wói cÖavb ÎæwU¸‡jv e¨vL¨v Ki‡Z cvi‡eb|

5. Av‡jvK iwk¥i wµqv †iLv AsKb K‡i `„wói ÎæwU cÖwZKv‡i †j‡Ýi e¨envi e¨vL¨v Ki‡Z cvi‡eb|

6. ˆ`bw›`b Rxe‡b Av‡jvi cÖwZmi‡Yi e¨envi eY©bv Ki‡Z cvi‡eb|

10.6.1 †PvL I Zvi wµqv (Eye and Its Function) Avgv‡`i gyL gÛ‡ji `yw`‡K ywU Pÿz †KvU‡ii g‡a¨ Av‡Q GK †Rvov †PvL| GB †PvL w`‡q Avgiv

†`wL| †PvL wKfv‡e KvR K‡i ev Avgiv wKfv‡e †`wL eyS‡Z n‡j †Pv‡Li MVb m¤ú‡K© Rvb‡Z n‡e|

wb‡Pi 10.25 bs wP‡Î †Pv‡Li wewfbœ Ask †`Lvb n‡q‡Q| GKwU k³ †Mvj‡Ki g‡a¨ wewfbœ ˆRe c`v‡_©i

mgš‡q Pÿz MwVZ, †MvjKwUi bvg Awÿ †MvjK| †MvjKwUi evB‡ii Ask GKwU k³ mv`vi‡Oi A¯”Q Zš‘ w`‡q

Ave„Z, GB AveiYxi bvg †k¦ZgÛj| †k¦ZgÛ‡ji mvg‡b LvwbKUv Ask DËj I ¯”Q, GB As‡ki bvg Kwb©qv|

†k¦ZgÛ‡ji †fZ‡ii Mv‡q Kv‡jv i‡Oi Av¯ÍiY _v‡K GK e‡j K…ògÛj| Kwb©qvi †cQ‡b GKwU GB A¯”Q

AveiYx‡K e‡j AvBwik|

AvBwik †Pv‡Li Dci cwZZ Av‡jv wbqš¿Y K‡i|

wewfbœ gvby‡li AvBwi‡ki iO wewfbœ nq|

mvaviYZ iO¸‡jv Kv‡jv, bxj ev ev`vgx nq|

Awÿ‡Mvj‡Ki †fZ‡ii c„‡ô †Mvjvcx i‡Oi

Cl`”Q Av‡jvK ms‡e`b AveiY‡K †iwUbv e‡j|

GwU iW Ges †Kvb bv‡g KZ¸‡jv ¯œvqyZš‘ Øviv

MwVZ Ges G¸‡jv Pÿz ¯œvqyi mv‡_ mshy³ _v‡K|

wPÎ t 10.25 gvbe Pÿzi MVb

AvBwi‡ki gvSLv‡b GKwU †QvÆ wQ`ª _v‡K, GwU †Pv‡Li gwY ev Zviv iÜ«| Gi ga¨ w`‡q Av‡jv †Pv‡L cÖ‡ek K‡i|

Zviv i‡Ü«i †cQ‡b _v‡K Pÿz †jÝ| GwU ¯”Q, ‰Re c`v‡_©i ˆZwi GKwU DËj †jÝ| wmwjqvix †ckx I mvm‡cÝix

eÜbx Øviv AvUKv‡bv _v‡K|

†jÝ I KwY©qvi gv‡S duvKv hvqMvq GK ai‡bi ¯”Q jeYv³ Rjxq c`v‡_© c~Y© _v‡K| †jÝ I †iwUbvi gvSLv‡bi

duvKv hvqMvI Abyiƒcfv‡e GK ai‡Yi †Rwj RvZxq ¯^”Q c`v‡_© c~Y© _v‡K| G‡`i h_vµ‡g A¨vKzqvm wnDgvi Ges

wfwUªqvm wnDgvi ejv nq| KwY©qv, A¨vKzqvm wnDgvi, wfwUªqvm wnDgvi, Pÿy‡jÝ me wKQz wg‡j GK‡Î GKwU DËj

†j‡Ýi KvR K‡i| †Pv‡Li mvg‡b e¯‘ _vK‡j H e ‘ †_‡K cÖwZdwjZ Av‡jv Pÿz †j‡Ýi ga¨ w`‡q †iwUbvi Dci

c‡o Ges we¤ m„wó K‡i| Zv †_‡K gw¯Í‡®‹ `k©‡bi Abyf~wZ m„wó nq Ges Avgiv †`L‡Z cvB| Pÿz‡jÝ cÖ‡qvRb g‡Zv

¯qswµqfv‡e AvK…wZ †QvU eo K‡i| d‡j Gi †dvKvm `~iZ¡ Kg †ewk nq| †dvKvm `~iZ¡ cwieZ©‡bi d‡j jÿ¨e¯‘

†hLv‡bB _vKzK †iwUbvi Dc‡iB Zvi cÖwZwe¤ c‡o| Pÿy †j‡Ýi Gfv‡e †dvKvwms Kivi ÿgZv‡K Dc‡hvRb ÿgZv

e‡j|

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 236

Dc‡ii wP‡Î †`Lvb n‡q‡Q, jÿ¨e¯‘ †_‡K cÖwZdwjZ iwk¥¸”Q Pÿy ‡j‡Ýi ga¨ w`‡q †iwUbvq †dvKvm nq| H Av‡jv

¯œvqyZš‘‡Î GK cÖKvi D‡ËRbv m„wó K‡i d‡j gw¯Í‡®‹ `k©‡bi Abyf~wZ Rv‡M|

10.6.2 iwOb e ‘i Av‡jvKxq Dcjwä (Perception of Coloured Objects) Avgiv hLb †Kvb jÿ¨e¯‘i w`‡K ZvKvB ZLb H e¯‘ †_‡K Av‡jv Avgv‡`i †Pv‡L c‡o Pÿz †j‡Ýi ga¨w`‡q

cÖwZm„Z n‡q †iwUbvq c‡o| †iwUbvq wecyj msL¨K ¯œvqy _v‡K hviv gw¯Í‡®‹ Av‡jvi Abyf~wZ †cÖiY K‡i| gw¯Í®‹

we‡køl‡Yi gva¨‡g Avgv‡`i Abyf~wZ m„wó K‡i| †iwUbvi ¯œvqy Zš‘My‡jvi bvg iW (Rod) Ges †Kvb (Cone)| G‡`i

g‡a¨ wZb ai‡Yi †Kvb Av‡Q| wKQz bxj eY©, wKQz jvj eY© Ges wKQz meyR eY© ms‡e`bkxj| e¯‘i iO hvB †nvK bv

†Kb †Kvb¸‡jv Zv‡K GB wZbwU †gŠwjK i‡O aviY K‡i| aviY K„Z Z_¨ gw¯Í‡®‹ hvq| Ab¨w`‡K iW¸‡jv e¯‘i

bovPov mbv³ K‡i| gw¯Í®‹ mKj e¯‘i eY© I MwZwewa we‡kølY K‡i Avgv‡`i Abyf~wZ m„wó K‡i| Gfv‡e Avgv‡`i

†PvL e¯‘i MwZkxjZv Ges eY© m¤ú‡K© ms‡e`bkxj nq|

10.6.3 †Pv‡Li Dc‡hvRb I ¯úó `k©‡bi by¨bZg `~iZ¡

Accommodation of Eye and Least Distance for Distinct Vision †Pv‡Li Dc‡hvRb t Avgiv Rvwb GKwU DËj †j‡Ýi mvg‡b Zvi †dvKvm `~i‡Z¡i evB‡i †h †Kv‡bv `~i‡Z¦ GKwU e¯‘

ivL‡j †j‡Ýi †cQ‡b e¯‘wUi GKwU ev¯Íe I D‡ëv cÖwZwe¤ m„wó nq| †cQ‡b GKwU c`©v ivL‡j c`©vi Dci H we¤wU

†`Lv hvq| cixÿv K‡i †`Lv †M‡Q e ‘ ~iZ¡ cwieZ©b n‡j my®úó we‡¤i Rb¨ c`©vwUi Ae¯’vb cwieZ©b Ki‡Z nq|

c`©vwU GKB RvqMvq †i‡L wewfbœ `~i‡Z¡i e¯‘i ¯úó we¤ †c‡Z n‡j †j‡Ýi †dvKvm `~iZ¡ cwieZ©b Ki‡Z nq, A_©vr

Avjv`v Avjv`v †dvKvm ~i‡Z¡i †jÝ e¨envi Ki‡Z nq| Avgiv wbqZ wewfbœ `~i‡Z¡i e¯‘ †`wL, A_P Avgv‡`i

†Pv‡Li †j‡Ýi †Kvb cwieZ©b Ki‡Z nq bv| GKwU gvÎ Pÿy †jÝ w`‡q mewKQz †`Lv hvq| GwU A™¢zZ bq wK?

Kxfv‡e GwU m¤¢e nq?

†Pv‡Li KwY©qv, A¨vKzqvm wnDgvi, wfwUªqvm wnDgvi Ges Pÿz †jÝ g~jZ GK m‡½ GKwU †j‡Ýi KvR K‡i| GB

mw¤§wjZ †j‡Ýi we‡kl ¸Y n‡jv cÖ‡qvRb gZ Gi AvK…wZ cwieZ©b K‡i †dvKvm `~iZ¡ Kwg‡q evwo‡q wb‡Z cv‡i|

†dvKvm `~i‡Z¡i GB cwieZ©‡bi Kvi‡Y jÿ¨e¯‘ †h †Kvb `~i‡Z¡ _vKzK bv †Kb †jÝ Z`vbyhvqx †dvKvm `~iZ¡ mgšq

K‡i †iwUbvi Dci ¯úó cÖwZwe¤ MVb K‡i| †h †Kvb `~i‡Z¡i e¯‘ †`Lvi Rb¨ †Pv‡Li †j‡Ýi †dvKvm `~iZ¡ mgš‡qi

GB ÿgZv‡K †Pv‡Li Dc‡hvRb ÿgZv ev ms‡ÿc Dc‡hvRb ejv nq|

¯úó `k©‡bi by¨bZg ev wbKUZg `~iZ¡ t eB‡qi c„ôvwU mvg‡b aiæb Ges c„ôvwUi Dci ZvKvb| Aÿi¸‡jv †`Lyb|

c„ôvwU Av‡¯Í Av‡¯Í `~‡i wbb| Kx †`L‡Qb ? cvZvwU hZ `~‡i hvq Aÿi¸‡jv ZZ †QvU n‡Z _v‡K Ges GK mgq

A¯úó n‡q hvq| wKš‘ e¯‘i AvKvi eo n‡j Zv A¯úó nq bv †Kej †QvU nq| Gevi c„ôvwU µgk mvg‡bi w`‡K

Avb‡Z _vKzb| GK mgq †`L‡eb my®úó Aÿi¸‡jv Avevi A¯úó n‡q hv‡”Q, co‡Z Kó n‡”Q| A_©vr †Pv‡Li

mvg‡b GKUv wbw`©ó `~iZ¡ ch©šÍ Aÿi¸‡jv Lye ¯úó †`Lv hvq| †h wbKUZg `~iZ¡ ch©šÍ †PvL webv kÖvwšÍ‡Z ¯úó

†`L‡Z cvq Zv‡K ¯úó `k©‡bi by¨bZg ev wbKUZg `~iZ¡ e‡j| ¯vfvweK †Pv‡Li Rb¨ ¯úó `k©‡bi by¨bZg

(wbKUZg) `~iZ¡ 25 †mwg| A_©vr †Pv‡Li †jÝ †_‡K 25 †mw›UwgUvi `~ieZx© we›`y‡Z ¯’vwcZ e¯‘wU‡K my›`i

my¯úófv‡e †`Lv hvq|Gi †_‡K Kg ~i‡Z¡ ¯’vwcZ e ‘ ¯úó †`Lv hvq bv|

10.6.4 †Pv‡Li ÎæwU I Zvi cÖwZKvi (Defects of Vision and their Remedy) Avgiv Av‡Mi Aby‡”Q‡` Rvbjvg ¯vfvweK †Pv‡Li `„wói mxgv †Pv‡Li mvg‡b 25 †mw›UwgUvi †_‡K Amxg ch©šÍ

(hw`I `~‡ii e¯‘ †QvU †`Lv hvq)| GB `~iZ¡‡K †Pv‡Li cvjøv e‡j|hw` †Kv‡bv †PvL GB cvjøvi g‡a¨ †Kv‡bv e¯‘‡K

¯úó †`L‡Z bv cvq, Zv n‡j †mB †PvL‡K ÎæwUc~Y© ejv nq| †Pv‡L cÖavbZ: `y ai‡Yi ÎæwU †`Lv hvqÑ n« `„wó ev

wbKU e× `„wó Ges `xN© „wó ev ~i e× „wó|

c`v_©weÁvb

BDwbU 10 c„ôv # 237

1. n« „wó ev wbKU e× „wó ev gvBIwcqv (Short sight or Myopia) GB ÎæwUMÖ ’ gvbyl `~‡ii e¯‘ fvjfv‡e †`L‡Z cv‡i bv, Z‡e Kv‡Qi e¯‘ fvjfv‡e †`L‡Z cvq| †Pv‡Li ¯úó `k©‡bi

by¨bZg `~iZ¡ ev wbKU `~iZ¡ K‡g hvq| wbKU we›`y †Pv‡Li mvg‡b P‡j Av‡m| Pÿz‡Mvj‡Ki e¨vmva© †e‡o †M‡j ev

†Pv‡Li †j‡Ýi †dvKvm `~iZ¡ K‡g †M‡j GB ÎæwU †`Lv †`q|

GB ÎæwUi d‡j `~i †_‡K AvMZ iwk¥¸”Q Pÿz †j‡Ýi ga¨ w`‡q cÖwZm„Z n‡q

†iwUbvi mvg‡b GKwU we›`y‡Z wgwjZ nq, d‡j †iwUbvi cwie‡Z© Av‡MB

cÖwZwe¤ MwVZ nq| D`vniY ¯iƒc wPÎ 10.26 (K) †`Lvb n‡q‡Q P we›`y‡Z

cÖwZwe¤ MwVZ n‡q‡Q| d‡j †iwUbvq MwVZ we¤wU A¯úó n‡e| ZvB †PvL

`~‡ii e¯‘ ¯úó †`L‡Z cvq bv|

GB ÎæwU `~i Kivi Rb¨ †Pv‡L Pkgv ev K›Uv± †jÝ e¨envi Kiv nq| G‡ÿ‡Î

ÎæwUi cwigvY hvPvB K‡i cÖ‡qvRbxq †dvKvm ˆ`‡N© i ev cvIqv‡ii AeZj

†jÝ e¨envi Kiv nq| AeZj †jÝ jÿ¨e¯‘ †_‡K AvMZ iwk¥‡K cwigvY g‡Zv

Qwo‡q †`q, d‡j †dvKvm †iwUbv‡Z c‡o Ges e¯‘i my¯úó we¤ ˆZwi nq| wPÎ

10.26 (L) †`Lvb n‡q‡Q| G‡ÿ‡Î †jÝ †Pv‡Li wbKU we›`y †cQ‡b mwi‡q

†`q|

wPÎ t 10.26 n« `„wó I Zvi

cÖwZKvi

2. `xN© `„wó ev ~i e× `„wó ev nvBcvi‡g‡Uªvwcqv (Long sight or Hypermetropia) GB ÎæwUMÖ ’ gvbyl `~‡ii e¯‘ fvjfv‡e †`L‡Z cv‡i, wKš‘ Kv‡Qi e¯‘ fvjfv‡e †`L‡Z cv‡i bv| †Pv‡Li ¯úó `k©‡bi

wbKU `~iZ¡ ~‡i m‡i hvq ev †e‡o hvq| Pÿz †Mvj‡Ki e¨vmva© K‡g †M‡j ev †Pv‡Li †j‡Ýi †dvKvm `~iZ¡ †e‡o

†M‡j GB ÎæwU †`Lv †`q|

wPÎ t 10.27 `xN© „wó I Zvi

cÖwZKvi

GB ÎæwUi d‡j †Pv‡Li Kv‡Qi jÿ¨e¯‘ †_‡K AvMZ iwk¥¸”Q Pÿz †j‡Ýi ga¨

w`‡q cÖwZm„Z n‡q †iwUbvi †cQ‡b GKwU we›`y‡Z wgwjZ nq, d‡j †iwUbvi

cwie‡Z© †cQ‡b cÖwZwe¤ MwVZ nq| D`vniY ¯^iƒc wPÎ 10.27 (K) †`Lvb

n‡q‡Q P we›`y‡Z cÖwZwe¤ MwVZ n‡q‡Q| d‡j †iwUbvq MwVZ we¤wU A¯úó nq|

ZvB †PvL Kv‡Qi e¯‘ ¯úó †`L‡Z cvq bv|

GB ÎæwU `~i Kivi Rb¨I †Pv‡L Pkgv ev K›Uv± †jÝ e¨envi Kiv nq| G‡ÿ‡Î

ÎæwUi cwigvY hvPvB K‡i cÖ‡qvRbxq †dvKvm ˆ`‡N© i ev cvIqv‡ii DËj †jÝ

e¨envi Kiv nq| DËj †jÝ jÿ¨e¯‘ †_‡K AvMZ iwk¥‡K cwigvY g‡Zv

msKzwPZ K‡i, d‡j †dvKvmwU †iwUbv‡Z c‡o Ges e¯‘i my¯úó we¤ ˆZwi nq|

wPÎ 10.27 (L) †`Lvb n‡q‡Q| G‡ÿ‡Î †jÝ †Pv‡Li wbKU we›`ywU mvg‡b

GwM‡q Av‡b| 10.27 K-wP‡Î cÖ_‡g GKwU ÎæwUc~Y©© †PvL Ges 10.27 L-wP‡Î

Pkgv e¨env‡ii d‡j ÎæwU gy³ „wó †`Lvb n‡q‡Q|

10.6.5 ˆ`bw›`b Rxe‡b Av‡jvi cÖwZmi‡Yi e¨envi (Uses of refraction of light in our daily life) Avgv‡`i ˆ`bw›`b Rxe‡b Av‡jvi cÖwZmi‡Yi cÖfve Acwimxg| Avgiv ÁvZ A_ev AÁvZ fv‡eB Av‡jvi

cÖwZmiY‡K Rxe‡b Anin Kv‡R jvMvw”Q| wb‡P GmsµvšÍ K‡qKwU mvaviY NUbv D‡jøL Kiv n‡jv|

1. evqy Ges k~b¨ gva¨‡gi ga¨w`‡q cÖwZmwiZ my‡h©i Ges P‡›`ªi Av‡jv wbqZ c„w_ex‡Z co‡Q hv Avgv‡`i Rxeb

aviYv I cwiPvj‡bi me‡P‡q ¸iæZ¦c~Y© Aej¤b|

2. m~h©v¯Í Ges m~‡h©v`‡qi mgq m~h©wU‡K wekvj _vjvi gZ †`wL, evqy ͇ii ga¨ w`‡q Av‡jvi cÖwZmi‡Yi Kvi‡Y

Ggb nq|

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 238

3. Kv‡Pi `iRv, Rvbvjvi ga¨ w`q Av‡jv cÖwZmwiZ nq hv Avgiv wewfbœfv‡e e¨envi Kwi|

4. GKBfv‡e wbivcËvi Kvi‡Y evwZi XvKbv, jÚ‡bi wPgwb, ˆe`y¨wZK evj‡e Kv‡Pi AveiY w`‡q †X‡K wb‡q

e¨envi KiwQ| wKš‘ Av‡jvi cÖwZmiY bv n‡j GwU m¤¢e nZ wK?

5. wewfYœ ai‡Yi Av‡jvK msµvšÍ hš¿cvwZ ˆZwi‡Z Ges e¨env‡i cÖwZmi‡Yi cÖfve Kvh©Ki fv‡e AbymiY Kiv

nq|

6. Pkgv, `~iexÿY, evB‡bvKzjvi, gvB‡µv‡¯‹v‡ci, K¨v‡giv Kvh©cÖYvjx Av‡jvi cÖwZmi‡Yi bxwZ‡K Kv‡R jvMv‡bv

nq|

7. wcÖR‡gi ga¨w`‡q Av‡jv cÖwZmiY NwU‡q eY©vjx we‡kølY Kiv nq|eY©vjx we‡køl‡Yi Rb¨ M‡elYvMv‡q e¨eüZ

h‡š¿i bvgeY©vjx exÿY hš¿| GB hš¿ gnvKvk M‡elYv †_‡K ïiæ K‡i ÿz`ªvwZÿz`ª cigvYyi ˆewkó¨ M‡elYvq

e¨eüZ nq|

8. cvwbi Zjvq †Kvb e¯‘i cÖK…Z Ae ’v mbv³ Ki‡Z cÖwZmi‡Yi Ávb I AwfÁZv Kv‡R jv‡M| cÖwZmi‡Yi

Kvi‡Y ¯”Q cvwbi cyKzi ev Rjvk‡qi Zjvi RjR Dw™¢ cÖvYx GgbwK cvwbi Zjvi f~wg‡KI DuPz‡Z †`Lv hvq|

9. GKwU mij `Û‡K KvZ K‡i cvwb‡Z ivL‡j euvKv †`Lvq| GKwU wbgw¾Z gy`ªv‡K Dc‡i †`Lv hvqÑ Av‡jvi

cÖwZmi‡Yi cÖfv‡e| cÖwZmi‡Yi Ávb‡K Kv‡R jvwM‡q G‡`i mwVK Ae¯’vb eyS‡Z nq| AvcwbI G ai‡bi

AviI A‡bK D`vniY w`‡Z cvi‡eb|

10. AvKv‡ki Zviv¸‡jv‡K Avgiv wgU wgU Ki‡Z †`wL| evqygÛ‡ji wewfbœ ¯Í‡ii ga¨ w`‡q Av‡jvi cÖwZmi‡Yi

ZviZg¨ Gi KviY|

11.AcwUK¨vj dvBev‡ii ga¨ w`‡q Av‡jvi cÖwZmiY‡K Kv‡R jvwM‡q †UwjKwgDwb‡Kkb, wPwKrmv e¨e¯’v, †mÝi I

Av‡jvK m¾vq cÖf~Z Dbœqb I AMÖMwZ mvwaZ n‡”Q|

mvi-ms‡ÿc:

Dc‡hvRb ÿgZvt †h †Kv‡bv `~i‡Z¡i e¯‘ †`Lvi Rb¨ †Pv‡Li †j‡Ýi mqswµqfv‡e †dvKvm `~iZ¡ mgš‡qi ÿgZv‡K

†Pv‡Li Dc‡hvRb ÿgZv ev ms‡ÿc Dc‡hvRb ejv nq|

¯úó `k©‡bi wbKUZg `~iZ¡ t †h wbKUZg ~iZ¡ ch©šÍ †PvL webv kÖvwšÍ‡Z ¯úó †`L‡Z cvq Zv‡K ¯úó `k©‡bi

b~¨bZg ev wbKUZg `~iZ¡ e‡j| ¯vfvweK †Pv‡Li Rb¨ ¯úó `k©‡bi b~¨bZg (wbKUZg) ~iZ¡ 25 †mwg|

cv‡VvËi g~j¨vqb -10.6

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| gvbe Pÿzi †k¦ZgÛ‡ji Ae¯’vb †Kv_vq?

(K) Pÿz †KvU‡ii evB‡i (L) Pÿz †Mvj‡Ki evB‡i

(M) Pÿz †Mvj‡Ki †fZ‡i (N) Pÿz †Mvj‡Ki mvg‡b

2| †iwUbvi iW¸‡jvi KvR wK?

(K) e ‘i iO ev eY© mbv³ Kiv (L) e¯‘i D¾¡jZv mbv³ Kiv

(M) e¯‘i ~iZ¡ mbv³ Kiv (N) e¯‘i bovPov mbv³ Kiv

3| ¯vfvweK †Pv‡Li ¯úó `k©‡bi b~ bgZ `~iZ¡ KZ?

(K) 0.25 wgUvi (L) 0.025 wgUvi

(M) 25 wgUvi (N) 0.25†mw›UwgUvi

c`v_©weÁvb

BDwbU 10 c„ôv # 239

cvV -7t e¨envwiK-12 DËj †jÝ e¨envi K‡i cÖwZwe¤ m„wó

To create an image using convex lens

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. DËj †jÝ e¨envi K‡i ev Íe cÖwZwe¤ m„wó I cÖ k©b Ki‡Z cvi‡eb|

cÖ‡qvRbxq DcKiY t GKwU DËj †jÝ A_ev g¨vMwbdvBs Møvm|

Kv‡Ri aviv t

1| GKwU DËj †jÝ ev g¨vMwbdvBs Møvm nv‡Z wbb| N‡ii evB‡i eviv›`vq ev N‡ii g‡a¨ †Lvjv Rvbvjvi

mvg‡b wM‡q `vuovb|

2| eviv›`vq uvov‡j N‡ii †`qv‡ji mvg‡b (N‡ii g‡a¨ `uvov‡j, †cQ‡b GK LÛ mv`v KvM‡Ri UzK‡ivi mvg‡b)

†jÝwU Ggb fv‡e mgvšÍivj K‡i aiæb †hb N‡ii evB‡ii †Kv‡bv jÿ¨e¯‘ †_‡K †j‡Ýi Dci Lvovfv‡e

GK¸”Q mvšÍivj Av‡jv G‡m co‡Z cv‡i| evB‡ii †Kvb MvQ cvjv, `vjvb BZ¨vw` …k¨‡K jÿ¨e¯‘ wbe©vPb

Ki‡Z cv‡ib|

3| †jÝwU‡K Wv‡b- ev‡g Nywi‡q †`qvj ev mv`v KvM‡Ri Dci

jÿ¨eš‘i GKwU cÖwZwe¤ †djyb|

4| †jÝwU‡K mvg‡b †cQ‡b mwi‡q †`qv‡ji cÖwZwe¤wU my¯úó

Kiæb| †Kvb GKwU wbw`©ó ¯’v‡b e ‘i we¤wU my¯úó n‡e|

mKj‡K GwU †`Lvb|

5| Gfv‡e †`qv‡j ev KvM‡Ri c`©vq ~‡ii jÿ¨ e¯‘i my¯úó

cÖwZwe¤^ cÖ k©b Kiv hvq|

wPÎ 10.28

6| iwk¥wPÎ Gu‡K cÖwZwe¤wUi MVb wPÎ AvuKzb I e¨vL¨v Kiæb

mZK©Zv t

(K) jÿ¨ ivL‡eb †`qv‡ji ev KvM‡Ri Zj mv`v, gm„Y Ges †j‡Ýi Z‡ji mv‡_ mgvšÍivj nq| (L) jÿ¨e¯‘wU

ch©vß Av‡jvwKZ _v‡K Ges we¤ m„wói hvqMvwU A‡cÿvK…Z Kg Av‡jvwKZ _v‡K|

https://www.youtube.com/watch?v=ZuBF4LNmC68

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 240

cvV -8t e¨envwiK-13 wewfbœ e¨w³i †Pv‡Li ¯úó `k©‡bi wbKUZg ~iZ¡ wbY©q

To Determine the near vision of different persons

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb

1. ¯úó `k©‡bi wbKUZg `~iZ¡ cwigvc K‡i †Pv‡Li ÎæwU wPwýZ Ki‡Z cvi‡eb|

cÖ‡qvRbx DcKiY : GK UzKiv Le‡ii KvMR ev †h ‡Kvb gyw`ªZ eB‡qi GKwU c„ôv ev Le‡ii KvMR,

GKwU †mw›UwgUv‡i `vMvw¼Z †¯‹j ev wdZv|

Kv‡Ri aviv t

1. Avcbvi cwievi I cÖwZ‡ewk‡`i g‡a¨ wewfbœ eq‡mi 7/8 Rb gvbyl †e‡Q wbb|

2. Avcbvi LvZvq wb‡Pi Q‡Ki g‡Zv GKwU ch©‡eÿY QK ˆZwi Kiæb||

3. GK GK Rb‡K †Pqv‡i ewm‡q cÖ‡Z¨K‡K wba©vwiZ Le‡ii

KvMR ev eB‡qi c„ôvwU co‡Z w`b| Gevi GK †PvL eÜ K‡i

co‡Z ejyb|

4. whwb †h Ae¯’v‡b †i‡L co‡Z ¯v”Q›`¨ †eva K‡ib †mB

Ae¯’v‡b KvMRwU a‡i ivL‡Z w`b|

5. †mw›UwgUvi †¯‹‡j †PvL †_‡K KvM‡Ri `~iZ¡ (j¤fv‡e) cwigvc

K‡i Q‡K wjLyb| GwUB Zvi H†Pv‡Li ¯úó `k©‡bi wbKUZg

`~iZ¡|

wPÎ t 10.29

6. cÖ_g ev‡i †Lvjv †PvLwU eÜ K‡i Gevi Ab¨ †PvLwU w`‡q †`L‡Z ejyb Ges GKBfv‡e wØZxq†Pv‡Li ¯úó

`k©‡bi wbKUZg `~iZ¡ †iKW© Kiæb|

7. whwb Pkgv c‡ib Zvi Pkgvmn Ges Pkgv Qvov `yfv‡eB cwigvc wbb Ges †iKW© Kiæb|

8. QK †_‡K eqm Abyhvqx ¯úó `k©‡bi wbKU we›`y m¤ú‡K© Avcvi gZvgZ wjLyb| hviv Pkgv c‡ib bv Zv‡`i

¯úó `k©‡bi Mo gvb †ei Kiæb|

9. Pkgvmn Ges Pkgv Qvov ¯úó `k©‡bi wbKU we›`yi wK ZviZg¨ Av‡jvPbv Kiæb|

ch©‡eÿY QK

µwgK

bs

eqm

(eQ‡i)

¯úó `k©‡bi wbKUZg `~iZ¡

(Pkgvmn)

¯úó `k©‡bi wbKUZg `~iZ¡

(Pkgv Qvov)

mycvwikK…Z

Pkgv

( cÖ‡qvRb n‡j)

Wvb

†PvL

evg

†PvL

Mo `~iZ¡ Wvb †PvL evg †PvL Mo `~iZ¡

mZK©Zv t

(K) cixÿY Kv‡j †¯‹j w`‡q gvcvi mgq †hb †Pv‡L †LvPv bv jv‡M †mw`‡K mZK© _vK‡Z n‡e| (L) †Pv‡Li †_‡K

KvM‡Ri wc‡Vi cwigvc Aek¨ j¤fv‡e wb‡Z n‡e|

(M) hviv co‡Z cv‡ib bv Zv‡`i Rb¨ Qwe hy³ KvW© e¨envi Kiæb|

c`v_©weÁvb

BDwbU 10 c„ôv # 241

P‚ovšÍ g~j¨vqb-10

K. mvaviY eûwbe©vPbx cÖkœ

mwVK Dˇii cv‡k wUK () wPý w`b|

1| †Kvb e‡Y©i Av‡jvi cÖwZmiYv‡¼i gvb me‡P‡q Kg?

(K) jvj (L) njy`

(M) †e¸wb (N) Kgjv

2&| cÖwZmiYv‡¼i GKK †KvbwU?

(K) wgwj wgUvi (L) wgD

(M) wWwMÖ (N) GKK bvB

3| ÔaÕ gva¨g ‡_‡K AvcwZZ iwk¥ ÔbÕ gva¨‡gi g‡a¨ Awfj‡¤i w`‡K †eu‡K †M‡j †KvbwU mwVK?

(K) aμ b > 1 (L) a μ b < 1

(M) aμ b =1 (N) a μ b = b μ a 4| AcwUK¨vj dvBev‡ii ga¨ w`‡q †Kvb kw³ cÖevwnZ nq?

(K) Zvc (L) Av‡jv

(M) we`y¨r (N) hvwš¿K

5| †KvbwU c~Y© Af¨šÍixY cÖwZdjb msMwVZ nIqvi kZ©?

(K) AvcZb †KvY > cÖwZmiY †KvY μ(L) AvcZb †KvY = vwšÍ †KvY

μ(M) AvcZb †KvY > vwšÍ †KvY μ(N) AvcZb †KvY < vwšÍ †KvY

L. eûc`x mgvwß m~PK cÖkœ t

1| †Uwj‡hvMv‡hv‡M AcwUK¨vj dvBev‡ii e¨env‡ii KviY Ñ

i. Gi ga¨ w`‡q ‡cÖwiZ Z_¨ AcPq nqbv|

ii. GwU ZvwoZ‡PŠ¤Kxq cÖfve gy³|

iii. Acv‡ikb QvovB †`‡ni †fZ‡ii Ask¸‡jv †`Lv hvq|

†KvbwU mwVK?

K) i I ii L) ii I iii M) iii I i N) i, ii I iii

M. Awfbœ Z_¨ wfwËK eûwbe©vPbx cÖkœ t

cv‡ki wP‡Î LL' GKwU DËj †jÝ| C Gi Av‡jvK †K› ª,

F cÖavb †dvKvm Ges F΄CF cÖavb A¶| †jÝwUi mvg‡b

cÖavb A‡¶i Ici A we›`y‡Z j¤fv‡e ’vwcZ AO GKwU

we¯Í……Z j¶¨e¯‘| BI e ‘wUi cÖwZwe¤|

wPÎwU ch©‡eÿY Kiæb Ges wb‡Pi cÖkœ ‡jvi DËi w`b|

1| MwVZ cÖwZwe¤wUi ˆewkó¨ wK?

(K) Am` I D‡ëv (L) Am` I †mvRv

(M) m` I †mvRv (N) m` I D‡ëv

2| wP‡Îi LL' †jÝwU AeZj n‡j, MwVZ cÖwZwe¤wUi ˆewkó¨ wK n‡Zv?

(K) Am` I D‡ëv (L) Am` I †mvRv

(M) m` I †mvRv (N) m` I D‡ëv

GmGmwm †cÖvMÖvg

BDwbU 10 c„ôv # 242

N. m„Rbkxj cÖkœ - 1

wP‡Î †`Lv hv‡”Q GKwU DËj †j‡Ýi mvg‡b cÖavb A‡¶i

Dci 15 mm DuPz GKwU e¯‘ O| e¯‘wUi kxl© †_‡K †j‡Ýi

ga¨ w`‡q `ywU iwk¥i Mgb c_ †`Lv‡bv n‡q‡Q| †jÝwUi

†dvKvm we›`y `ywU F I F′| †jÝwUi †dvKvm `~iZ¡ 30 mm|

Ges †j‡Ýi Av‡jvK †K›`ª †_‡K e¯‘wUi `~iZ¡ 20 mm|

wb‡Pi cÖkœ ‡jvi DËi w`b Ges mgm¨v¸‡jvi mgvavb Kiæb|

(1) †j‡Ýi msÁv w`b|

(2) DËj †j‡Ýi ga¨w`‡q cÖwZmwiZ iwk¥ `ywU Acmvwi †Kb e¨vL¨v Kiæb|

(3) wPÎwU LvZvq Zz‡j m¤ú~Y© Kiæb| cÖwZwe¤wU †Kv_vq MwVZ n‡q‡Q Ges MwVZ cÖwZwe¤wUi ˆewk󨸇jv

wjLyb|

(4) weea©b ¶gZv wbY©‡qi m~ÎwU wjLyb| m¤ú~Y© wPÎ †_‡K MwVZ cÖwZwe¤wUi ˆ`N© wbY©q Kiv hv‡e wK?

wKfv‡e ? eY©bv Kiæb| cÖwZwe‡¤i ˆ`N© Ges weea©b wbY©q Kiæb|

N. MvwYwZK mgm¨v t

1| 45° AvcZb †Kv‡Y evqy gva¨g †_‡K cvwb gva¨‡g AvcwZZ mvaviY Av‡jvi cÖwZmiY †KvY 32° n‡j evqy

mv‡c‡¶ cvwbi cÖwZmiYv¼ wbY©q Kiæb|

2| †ebwR‡bi mv‡c‡¶ †K‡ivwm‡bi cÖwZmiYv¼ 0.96| †ebwRb I †K‡ivwm‡bi we‡f` Z‡j †ebwR‡bi g‡a¨

AvcwZZ iwk¥i Rb¨ msKU †KvY KZ n‡e?

3| 50 cm †dvKvm `~iZ¡ wewkó DËj †j‡Ýi ¶gZv wbY©q Kiæb|

4| 25 cm †dvKvm `~iZ¡ wewkó AeZj †j‡Ýi ¶gZv wbY©q Kiæb|

6| †Kvb e¨w³ Pkgv wnmv‡e 20 cm †dvKvm `~i‡Z¡i GKwU AeZj †jÝ e¨envi K‡ib| †jÝwUi ¶gZv KZ?

eûwbe©vPbx cÖkœ I MvwYwZK mgm¨vmg~‡ni DËigvjv

cv‡VvËi g~j¨vqb 10.1- 1| (L) 2| (N)

cv‡VvËi g~j¨vqb 10.2- 1| (L) 2| (K) 3| (K)

cv‡VvËi g~j¨vqb 10.3- 1| (L) 2| (K) 3| (N)

cv‡VvËi g~j¨vqb 10.4- 1| (N) 2| (M) 3| (K)

cv‡VvËi g~j¨vqb 10.5- 1| (L) 2| (L)

cv‡VvËi g~j¨vqb 10.6- 1| (L) 2| (N) 3| (K)

P‚ovšÍ g~j¨vqb 10

K. mvaviY eûwbe©vPbx cÖkœ t 1| (K) 2| (N) 3| (K) 4| (L) 5| (M)

L. eûc`x mgvwß m~PK eûwbev©Pbx cÖkœ t 1| (L) 2| (K)

M. Awfbœ Z_¨ wfwËK eûwbe©vPbx cÖkœ t 1| (N)

m„Rbkxj cÖkœ t 2 (K) cvV-2 mvis‡k †`Lyb

(L) AvcZb we›`y‡Z j¤ G‡Ku iwk¥ wPÎ AvuK‡Z n‡e| wb‡R †Póv Kiæb|

(M) wb‡R wPÎ AuvKzb, `c©‡Yi †cQ‡b †mvRv,ewa©Z Am` ev Aev¯Í we¤ n‡e|

(N) mgxKiY 10.11 ev 10.14, mgm¨vwU mgvavb wb‡R Kiæb, (Dt 45mm) wUD‡Uvwiqvj K¬v‡m wkÿK‡K †`Lvb|

MvwYwZK mgm¨vi DËi 1| 1.33 2| 74° 3| +2D 4| -4D 5| -5D