c`v_©weÁvb

BDwbU 9 c„ôv # 189

BDwbU t 9

Av‡jvi cÖwZdjb

REFLECTION OF LIGHT

f‚wgKv

Av‡jvi wewfbœ a‡g©i g‡a¨ GKwU nj cÖwZdjb| we‡k¦i hv wKQz Avgviv †`wL meB Av‡jvi cÖwZdj‡bi Kvi‡Y|

†Kv‡bv Av‡jvK Drm †_‡K Av‡jv Ab¨ e¯‘i Dci c‡o cÖwZdwjZ n‡q Avgv‡`i †Pv‡L G‡m c‡o e‡jB Avgiv e¯‘

†`L‡Z cvB| Avgiv †h Avqbvq Avgv‡`i †Pnviv †`wL, ¯”Q w¯’i cvwbi Dci Avgv‡`i cÖwZwe¤^ †`wL ZvI

cÖwZdj‡bi Kvi‡Y| PKP‡K avZe c„ô, KvP c„ô, AwZ gm„Y Avmeve cÎ, w¯’i cvwb c„ô A‡bK e¯‘‡ZB Av‡jvi

cÖwZdjb N‡U| we‡kl fv‡e ˆZwi cÖwZdjK c„ô‡K `c©Y ejv nq| mgZj c„ô, †MvjK c„ô, ev eµZj c„ôI

cÖwZdjK wnmv‡e e¨eüZ nq| G BDwb‡U cÖwZdj‡bi cÖK…wZ, cÖwZdj‡bi m~Îvewj, wewfbœ cÖKvi `c©Y, `c©‡Y

wKfv‡e cÖwZwe¤ m„wó nq Ges wewfbœ cÖKvi `c©‡Yi m„ó cÖwZwe‡¤i AvK…wZ I cÖK…wZ wb‡q Av‡jvPbv Kiv n‡e|

cvV-1 Av‡jvi cÖwZdjb (Reflection of Light)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

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

2. cÖwZdj‡bi m~Î eY©bv I e¨vL¨v Ki‡Z cvi‡eb|

3. cÖwZwe¤ e¨vL¨v Ki‡Z cvi‡eb|

9.1.1 Av‡jvi cÖwZdjb (Reflection of Light) Avgiv Rvwb †Kv‡bv Drm †_‡K wbM©Z Av‡jvK iwk¥ †h †Kv‡bv ¯”Q c`v‡_©i ga¨ w`‡q †h‡Z cv‡i| †h me

c`v‡_©i ga¨ w`‡q Av‡jvK iwk¥ †h‡Z cv‡i †m me c`v_©‡K ejv nq Av‡jvK ¯^”Q gva¨g| Avevi †h me c`v‡_©i

ga¨ w`‡q Av‡jvK iwk¥ †h‡Z cv‡i bv †m me c`v_©‡K ejv nq Av‡jvK A¯”Q gva¨g| c`v‡_©i ga¨ w`‡q Av‡jvK

iwk¥i Mg‡bi ¯”Q›` Abymv‡i A_v©r Av‡jvK ¯”QZv wePv‡i mKj c`v_©‡K wZb fv‡M fvM Kiv nq - ¯”Q, A¯”Q

Ges Cl`”Q| †h †Kvb ¯”Q gva¨‡gi ga¨ w`‡q Av‡jv iwk¥ †mvRv mvg‡b A_©vr, mij †iLvq GwM‡q P‡j| mvaviYZt

Pjvi c‡_ iwk¥wU hw` †Kvb Av‡jvK A¯”Q gva¨g Øviv evav cÖvß nq Zvn‡j yB gva¨‡gi we‡f` Zj †_‡K c~e©eZx

¯^”Q gva¨‡gi g‡a¨ wd‡i Av‡m Ges Avevi †mvRv c‡_ Pj‡Z _v‡K| A‡bK mgq †`Lv hvq we‡klfv‡e cwZZ n‡j

¯”Q gva¨g Zj †_‡KI Av‡jvK iwk¥ Av‡Mi gva¨‡g AvswkK ev m¤ú~Y© wd‡i Av‡m| Av‡jvi iwk¥i Gfv‡e evav

†c‡q Av‡Mi gva¨‡g wd‡i Avmvi cÖwµqvwU Av‡jvi cÖwZdjb|

cÖwZdj‡bi msÁv t †Kv‡bv Av‡jvK iwk¥ †Kv‡bv ¯^”Q gva¨‡gi ga¨ w`‡q hvIqvi mgq Ab¨ †Kv‡bv gva¨g Øviv evav

cÖvß n‡j yB gva¨‡gi we‡f`Zj †_‡K cÖ_g gva¨‡g wd‡i Av‡m| Av‡jvi GB wd‡i Avmvi cÖwµqv‡K Av‡jvi

cÖwZdjb e‡j|

†h we‡f` Zj †_‡K Av‡jv wd‡i Av‡m Zv‡K cÖwZdjK Zj ev cÖwZdjK c„ô e‡j, Avi c~e©eZx© gva¨‡g wd‡i Avmv

Av‡jv‡K ejv nq cÖwZdwjZ Av‡jv ev iwk¥| mvaviYZt `yB gva¨‡gi we‡f` Z‡j †h cwigvY Av‡jv G‡m c‡o

memgq Zv m¤ú~Y© cÖwZdwjZ nq bv| cwZZ Av‡jvi KZUzKz cÖwZdwjZ n‡e Zv ywU wel‡qi Dci wbf©i K‡i | Zv

n‡jv,-

1. gva¨g `ywUi cÖK…wZ Ges

2. AvcwZZ Av‡jv cÖwZdjK Z‡ji Dci KZ †Kv‡Y AvcwZZ nq Zvi cwigvY|

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 190

cÖwZdjK Zj hZ †ewk gm„Y nq cÖwZdjb ZZ †ewk nq| Avevi A¯”Q cÖwZdj‡Ki †P‡q ¯”Q cÖwZdj‡K

cÖwZdjb Kg nq| †hgb mv`v Z‡j Av‡jvi cÖwZdjb †ewk nq| Kv‡jv i‡Oi Z‡j Av‡jvi cÖwZdjb nq bv ej‡jB

P‡j| KvP GKwU Av‡jvK ¯”Q gva¨g| Gi Dci Av‡jv AvswkK cÖwZdwjZ nq| Avevi Av‡jvK iwk¥ j¤^fv‡e co‡j

Lye mvgvb¨ cÖwZdwjZ nq| iwk¥ hZ †ewk †Kv‡Y AvcwZZ nq cÖwZdj‡bi cwigvYI ZZ †ewk nq| cÖwZdjb Z‡ji

gm„YZv Abyhvqx cÖwZdjb‡K `yÕfv‡M fvM Kiv n‡q‡Q ; Zv n‡jv-

1. wbqwgZ cÖwZdjb Ges

2. e¨vß cÖwZdjb|

†Kv‡bv mgZj `c©‡Yi Dci GK ¸”Q mgvšÍivj Av‡jvK iwk¥ AvcwZZ n‡j cÖwZdj‡bi ci iwk¥¸”Q mgšÍivj _v‡K

(wPÎ 9.1)| AeZj `c©‡Yi Dci mgšÍivj Av‡jvK iwk¥ AvcwZZ n‡j Awfmvix ev Acmvix iwk¥¸‡”Q cwiYZ nq|

wKš‘ Ge‡ov‡_e‡ov Z‡ji Dci mgvšÍivj iwk¥¸”Q cwZZ n‡q cÖwZdj‡bi c‡i mgšÍivj _v‡K bv, ev Awfmvix ev

Acmvix iwk¥‡ZI cwiYZ nq bv| eis Gw`K †mw`K wewÿßfv‡e A_©vr AwbqwgZfv‡e Qwo‡q c‡o (wPÎ 9.2)|

GKLÛ gm„Y ivsZv KvM‡Ri Dci m~h© iwk¥ †dj‡j Av‡jvK iwk¥i cÖwZdjb my®úófv‡e †`Lv hvq, wKš‘ GB ivsZv

KvM‡Ri UzK‡ivwU gy‡Vi g‡a¨ KzP‡K wb‡q Av‡jv‡Z a‡i †`Lyb †Kvb cÖwZdwjZ iwk¥ ‡`L‡Z cv‡eb bv| eyS‡ZB

cvi‡Qb, cÖ_g cÖKv‡ii cÖwZdjb n‡”Q wbqwgZ; Avi wØZxq cÖKvi cÖwZdjb AwbqwgZ ev e¨vß| Gevi Avmyb

Avgviv wbqwgZ cÖwZdjb Ges e¨vß cÖwZdj‡bi msÁv †`B|

wPÎ t 9.1 - wbqwgZ cÖwZdjb

wPÎ t 9.2 - e¨vß cÖwZdjb

wbqwgZ cÖwZdjb (Regular reflection)t hw` GK¸”Q mgvšÍivj Av‡jvK iwk¥ †Kv‡bv c„‡ô AvcwZZ n‡q

cªwZdj‡bi ci mgvšÍivj, Awfmvix ev Acmvix Av‡jvK ¸‡”Q cwiYZ nq Zv n‡j †mB cÖwZdjb‡K wbqwgZ

cÖwZdjb e‡j| cÖwZdjK c„ô gm„Y n‡j wbqwgZ cÖwZdjb nq| mgZj `c©Y, AeZj `c©Y, DËj `c©‡Y wbqwgZ

cÖwZdjb N‡U| G ‡ÿ‡Î me¸‡jv iwk¥i AvcZb †KvY Ges cÖwZdjb †KvY mgvb nq|

e¨vß cÖwZdjb (Diffused reflection)t hw` GK¸”Q mgvšÍivj Av‡jvK iwk¥ †Kv‡bv c„‡ô AvcwZZ n‡q cªwZdj‡bi

ci mgvšÍivj, Awfmvix ev Acmvix Av‡jvK ¸‡”Q cwiYZ bv nq Zv n‡j †mB cÖwZdjb‡K e¨vß cÖwZdjb e‡j|

cÖwZdjK c„ô gm„Y bv n‡j e¨vß cÖwZdjb N‡U| N‡ii †`qvj, KvMR, evwb©k bv Kiv †h †Kvb Kv‡Vi Dcwi Zj

BZ¨vw` c„ô Agm„Y Gme Z‡j e¨vß cÖwZdjb N‡U| G †ÿ‡Î me¸‡jv iwk¥i AvcZb †KvY ev cÖwZdjb †KvY

ci¯úi mgvb nq bv|

9.1.2 cÖwZdjb msµvšÍ K‡qKwU c‡`i msÁv (Some definitions) cÖwZdjK Zj (Reflecting surface)t Av‡jvK iwk¥ Mgb c‡_ †h gm„Y Z‡j evav †c‡q Av‡Mi gva¨‡g wd‡i hvq ev

cÖwZdwjZ nq Zv‡K cÖwZdjK Zj e‡j| 9.3 wP‡Î cÖwZdjK MM′ Zj †`Lv‡bv n‡q‡Q| (9.3 cÖwZdjK Z‡ji

wPÎ eySv‡Z Gi wb‡P wPiæbxi `v‡Zi g‡Zv †ZiQv Nb `vM KvUv nq)|

c`v_©weÁvb

BDwbU 9 c„ôv # 191

AvcwZZ iwk¥ (Incident ray) t †h iwk¥ cÖwZdjK Z‡ji Ici G‡m

c‡o Zv‡K AvcwZZ iwk¥ e‡j| wP‡Î AO AvcwZZ iwk¥ (wPÎ 9.3)|

(AvcZb Z‡ji w`‡K Zxi wPý w`‡q mij‡iLv Gu‡K AvcwZZ iwk¥

‡`Lv‡bv nq)|

AvcZb we›`y (Point of incidence)t cÖwZdj‡Ki Dci †h we›`y‡Z

AvcwZZ iwk¥ G‡m c‡o Zv‡K AvcZb we›`y e‡j| 9.3 wP‡Î O AvcZb we›`y|

wPÎ t 9.3 Av‡jvK iwk¥i cÖwZdjb

Awfj¤ (Normal) t AvcZb we›`y‡Z cÖwZdjK c„‡ôi Dci Aw¼Z j¤‡K Awfj¤ e‡j| 9.3 wP‡Î ON Awfj¤|

cÖwZdwjZ iwk¥ (Reflected ray) t cÖwZdjK Z‡j evav †c‡q †h iwk¥ Av‡Mi gva¨‡g wd‡i Av‡m Zv‡K cÖwZdwjZ

iwk¥ e‡j| 9.3 wP‡Î OB cÖwZdwjZ iwk¥| (AvcZb we›`y †_‡K †ewi‡q hvIqv Zxi wPý hy³ mij †iLv Gu‡K

cÖwZdwjZ iwk¥ eySv‡bv nq)|

AvcZb †KvY (Angle of incidence) t AvcwZZ iwk¥ I Awfj¤ AvcZb we›`y‡Z †h †KvY Drcbœ K‡i A_©vr

AvcwZZ iwk¥ Awfj‡¤^i mv‡_ †h †KvY Drcbœ K‡i Zv‡K AvcZb †KvY e‡j| 9.3 wP‡Î AON AvcZb †KvY|

AvcZb †KvY eySv‡Z mvaviYZ i cÖZxK e¨eüZ nq|

cÖwZdjb †KvY (Angle of reflection) t cÖwZdwjZ iwk¥ I Awfj¤ AvcZb we›`y‡Z †h †KvY Drcbœ K‡i A_©vr

cÖwZdwjZ iwk¥ Awfj‡¤i mv‡_ †h †KvY Drcbœ K‡i Zv‡K cÖwZdjb †KvY e‡j| 9.3 wP‡Î NOB cÖwZdjb

†KvY| cÖwZdjb †KvY eySv‡Z mvaviYZ r cÖZxK e¨eüZ nq|

9.1.3 Av‡jvi cªwZdj‡bi m~Î (Laws of Reflection) Av‡jvi cÖwZdjb `yÕwU m~Î †g‡b P‡j, G‡`i cÖwZdj‡bi m~Î e‡j| m~Î yÕwU n‡jv-

1. AvcwZZ iwk¥, AvcZb we›`y‡Z cÖwZdj‡Ki Dci AswKZ Awfj¤ Ges cÖwZdwjZ iwk¥ GKB mgZ‡j

_v‡K|

2. AvcZb †KvY Ges cÖwZdjb †KvY me© v mgvb nq| A_©vr AvcZb †KvY i Ges cÖwZdjb †KvY r n‡j,

i = r cÖwZwe¤ (Image) : Avqbvi mvg‡b `vuov‡j Avqbvi g‡a¨ Avgv‡`i cÖwZ”Qwe †`Lv hvq| Avqbvi mvg‡b GKwU

†gvgevwZ ev †h †Kv‡bv e¯‘ ai‡j Avqbvi †fZ‡i H †gvgevwZwU ev e¯‘wU †`Lv hvq (wPÎ 9.4)| GwU wKfv‡e nq?

Avgiv Rvwb e¯‘ †_‡K Av‡jv G‡m Avgv‡`i †Pv‡L co‡jB Avgiv e¯‘wU †`L‡Z cvB| hLb †Kv‡bv e¯‘ †_‡K mivmwi

Av‡jv †Pv‡L c‡o bv ZLb wK H e ‘wU †`Lv hvq? ej‡eb nu¨v, †ÿÎ we‡k‡l †`Lv hvq| †hgb Avqbvi g‡a¨ †`wL|

e¯‘ †_‡K mivmwi Av‡jv Avgv‡`i †Pv‡L bv c‡o hw` Ab¨ †Kv‡bv Z‡j cÖwZdwjZ n‡q ev Ab¨ †Kvb gva¨‡g

cÖwZmwiZ n‡q Avgv‡`i †Pv‡L cÖ‡ek K‡i Zv n‡j Avgiv e¯‘wU‡K †`L‡Z cvB| (c‡ii BDwb‡U cÖwZmiY m¤ú‡K©

we¯ÍvwiZ Av‡jvPbv n‡q‡Q)|

wKš‘ e¯‘wU‡K ZLb Zvi Avmj Ae¯’v‡b †`Lv hvq bv| †hgb Avgviv Avqbvq wb‡Ri

†h c«wZ”Qwe †`wL Zv †`wL Avqbvi †cQ‡b| GKwU †gvgevwZ Avqbvi mvg‡b ivL‡j

Zvi cÖwZ”QweI †`wL Avqbvi †cQ‡b| g‡b nq Avqbvi †cQ‡bi †Kvb GKwU wbw`©ó

Ae¯’vb ev we›`y‡Z Aew¯’Z e¯‘ †_‡K Av‡jv Avgv‡`i †Pv‡L G‡m co‡Q| GB

cÖwZ”QwewUB cÖwZwe¤ ev we¤^ (wPÎ 9.4)|

wPÎ t 9.4 Avqbvi g‡a¨

†gvgevwZi cÖwZ”Qwe

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 192

cÖwZwe‡¤i msÁv t †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK iwk¥ ¸”Q cÖwZdwjZ ev cÖwZmwiZ n‡q hw` wØZxq †Kv‡bv

we›`y‡Z wgwjZ nq ev wØZxq †Kv‡bv we› y †_‡K Acm„Z n‡”Q e‡j g‡b nq, Zv n‡j H wØZxq we› y‡K cÖ_g we› yi

cÖwZwe¤ ev ms‡ÿ‡c we¤^ e‡j|

mgZj `c©Y Ges †MvjKxq `c©‡Y Av‡jvi cÖwZdjb nq, Avevi ¯”Q gva¨‡g ev †j‡Ýi ga¨ w`‡q Av‡jv cÖwZmwiZ

nq| c‡ii BDwb‡U cÖwZmiY m¤ú‡K© we¯ÍvwiZ Av‡jvPbv Kiv n‡q‡Q| cÖwZdjb Ges cÖwZmiY Dfq †ÿ‡ÎB

cÖwZwe¤ MwVZ nq| KLbI jÿ¨e¯‘ †_‡K wbtm„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‡ÿ‡ÎI cÖwZwe¤ †`Lv hvq| G me

cÖwZwe‡¤i ˆewk‡ó¨i Dci wfwË K‡i cÖwZwe¤‡K `yÕfv‡M fvM Kiv n‡q‡Q| m` ev ev¯Íe cÖwZwe¤ Ges Am` ev

Aev¯Íe cÖwZwe¤|

1. m` cÖwZwe¤^ (Real Image) t †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK iwk¥ ¸”Q cÖwZdwjZ ev cÖwZmwiZ n‡q

hw` wØZxq †Kv‡bv we›`y‡Z wgwjZ n‡q cÖwZwe¤ MVb K‡i Z‡e Zv‡K m` ev ev Íe cÖwZwe¤ e‡j| AeZj

`c©‡Y Gai‡Yi m` cÖwZwe¤ MwVZ nq ( wPÎ 9.23, wPÎ 9.25 )|

2. Am` cÖwZwe¤^ (Virtual Image)t †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK iwk¥ ¸”Q cÖwZdwjZ ev cÖwZmwiZ n‡q

cÖK…Z c‡ÿ wØZxq †Kv‡bv we›`y‡Z wgwjZ nq bv wKš‘ wØZxq †Kv‡bv we›`y †_‡K Acm„Z n‡”Q e‡j g‡b nq,

ZLb H wØZxq we›`y‡Z cÖ_g we›`yi †h cÖwZwe¤ †`Lv hvq Zv‡K Am` ev Aev¯Íe cÖwZwe¤^ e‡j| mgZj

`c©‡Y (wPÎ 9.5 †_‡K 9.10), Ges DËj `c©‡Y (wPÎ 9.24, I 9.26) G ai‡Yi cÖwZwe¤ MVb †`Lv‡bv

n‡q‡Q|

m` I Am` we‡¤i cv_©K¨

m` cÖwZwe¤^ Am` cÖwZwe¤^

1. †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK iwk¥ ¸”Q

cÖwZdwjZ ev cÖwZmwiZ n‡q wØZxq †Kvb

we›`y‡Z wgwjZ n‡q m & cÖwZwe¤ MwVZ nq|

1. †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK iwk¥ ¸”Q

cÖwZdwjZ ev cÖwZmwiZ n‡q wØZxq †Kvb we›`y †_‡K

Acm„Z n‡”Q e‡j g‡b n‡j wØZxq we›`y‡Z Am`&

cÖwZwe¤^ MwVZ nq|

2. m` cÖwZwe¤ MV‡bi †ÿ‡Î cÖwZdwjZ ev

cªwZmwiZ Av‡jvK iwk¥¸‡”Qi cÖK…Z wgjb nq|

2. Am` cÖwZwe¤ MV‡bi †ÿ‡Î cÖwZdwjZ ev cªwZmwiZ

Av‡jvK iwk¥¸‡”Qi cÖK…Z wgjb nq bv|

3. †Pv‡L †`Lv hvq, c`©vq †djv hvq Ges ¯úk©

Kiv hvq|

3. †Pv‡L †`Lv hvq, wKš‘ c`©vq †djv ev ¯úk© Kiv hvq

bv|

4. AeZj `c©Y I DËj †jÝ Øviv m`& cÖwZwe¤

Drcbœ nq

4. me iKg `c©Y I †jÝ Øviv Am`& cÖwZwe¤ Drcbœ

nq|

mvi-ms‡ÿc:

cÖwZdjb t †Kv‡bv Av‡jvK iwk¥ †Kvb ¯^”Q gva¨‡gi ga¨ w`‡q hvIqvi mgq Ab¨ †Kv‡bv gva¨g Øviv evav cÖvß n‡j

`yB gva¨‡gi we‡f`Zj †_‡K cÖ_g gva¨‡g wd‡i Av‡m| Av‡jvi GB wd‡i Avmvi cÖwµqv‡K Av‡jvi cÖwZdjb e‡j|

Av‡jvi cÖwZdj‡bi m~Î t

1. AvcwZZ iwk¥, AvcZb we›`y‡Z cÖwZdj‡Ki Dci AswKZ Awfj¤ Ges cÖwZdwjZ iwk¥ GKB mgZ‡j _v‡K|

2. AvcZb †KvY Ges cÖwZdjb †KvY me© v mgvb nq| A_©vr AvcZb †KvY i Ges cÖwZdjb †KvY r n‡j,

i = r cÖwZwe¤ t †Kvb we›`y †_‡K wbtm„Z Av‡jvK iwk¥ ¸”Q cÖwZdwjZ ev cÖwZmwiZ n‡q hw` wØZxq †Kvb we›`y‡Z wgwjZ

nq ev wØZxq †Kvb we›`y †_‡K Acm„Z n‡”Q e‡j g‡b nq, Zv n‡j H wØZxq we›`y‡K cÖ_g we›`yi cÖwZwe¤ ev ms‡ÿ‡c

we¤^ e‡j|

c`v_©weÁvb

BDwbU 9 c„ôv # 193

cv‡VvËi g~j¨vqb-9.1

mwVK Dˇii cv‡k wUK () wPý w`b|

1| Av‡jvK iwk¥ Mgb c‡_ evav cÖvß n‡j c~‡e©i gva¨‡g wd‡i Avmvi cÖwµqv‡K wK e‡j?

(K) cÖwZmiY (L) cÖwZdjb

(M) e¨wZPvi (N) AcmiY

2| AvcZb †KvY i Ges cÖwZdjb †KvY r n‡j, †KvbwU mZ¨?

(K) i = r (L) i r (M) i > r (K) r > i

3| AeZj `c©‡Yi cÖavb A‡ÿi Dci †Kv_vq e¯‘ ivL‡j cÖwZwe¤ Am` nq?

(K) Amx‡g (L) †giæ I cÖavb †dvKv‡mi g‡a¨

(M) cÖavb †dvKv‡m (N) eµZvi †K› ª I cÖavb †dvKv‡mi g‡a¨

cvV-2 `c©Y I cÖwZwe¤ MVb (Mirror and Image Formation )

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. `c©Y Kv‡K e‡j I `c©‡Yi cÖKvi‡f` e¨vL¨v Ki‡Z cvi‡eb|

2. †MvjKxq `c©‡Yi †ÿ‡Î e¨eüZ c`mg~n e¨vL¨v Ki‡Z cvi‡eb|

9.2.1 `c©Y (Mirror) we‡klfv‡e cÖ ‘Z †h gm„Y Z‡j Av‡jvi wbqwgZ cÖwZdjb N‡U Zv‡K `c©Y e‡j| cÖvPxb Kv‡j gvwUi

cv‡Î ¯”Q cvwb †i‡L Zv `c©Y wnmv‡e e¨envi Kiv n‡Zv| ciewZ© hy‡M avZe c„ô‡K gm„Y K‡i `c©Y cÖ ‘Z nq| Z‡e

GB `c©Y wQj `yg©~j¨ Ges `yj©f| GK mgq gvbyl KvP Avwe®‹vi Kij Ges Kv‡Pi mgZj wmU cÖ ‘Z Ki‡Z wkLj|

Gi ci Kv‡Pi GK wc‡V avZzi cÖ‡jc jvwM‡q `c©Y ˆZwi Kij| cÖ_g w`‡K cÖ‡j‡ci Kv‡R iƒcv e¨envi Kiv n‡Zv|

ZvB GB cÖ‡jc †`qv‡K cviv jvMv‡bv ev wmjfvwis ejv n‡Zv| GL‡bv G‡K wmjfvwis ejv nq| Kv‡Pi †h wc‡V

cvi` jvMv‡bv nq Zvi wecixZ c„ô cÖwZdjK Zj wnmv‡e e¨eüZ nq, GB c„ô‡K `c©Y c„ô e‡j|

`c©Y cÖavbZ yÕai‡Yi | h_v-

1. mgZj `c©Y (Plane mirror)Ges

2. †MvjKxq `c©Y (Spherical mirror)

†MvjKxq mgZj `c©Y (Plane mirror) t `c©Y c„ô hw` mgZj nq A_©vr †Kv‡bv mgZj c„ô hw` cÖwZdjK wnmv‡e

e¨eüZ nq Ges Zv‡Z Av‡jvK iwk¥i wbqwgZ cÖwZdjb N‡U Z‡e Zv‡K mgZj `c©Y e‡j| Avgiv †Pnviv †`Lvi

Rb¨ cÖwZw`b †h Avqbv e¨envi Kwi, Pzj QvUvi †mjy‡b, Uq‡j‡U, †Wªwms †Uwe‡j †h Avqbv e¨eüZ nq Zv mgZj

`c©Y|

†MvjKxq `c©Y (Spherical mirror) t †h `c©‡Yi cÖwZdjK c„ô †Mvj‡Ki c„ô ev †MvjK c„‡ôi Ask we‡kl Zv‡K

†MvjKxq `c©Y e‡j| †MvjK c„‡ôi `yÕwU w`K; GKwU evB‡i Z_v ev DuPz wcV, Ab¨wU †fZ‡i Z_v wbPz wcV| hw`

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 194

cÖwZdjK wcVwU †Mvj‡Ki DuPz w`K nq Z‡e †mB †MvjKxq `c©Y‡K DËj `c©Y e‡j| hw` cÖwZdjK wcVwU †Mvj‡Ki

wbPz w`K nq Z‡e †mB `c©Y‡K AeZj `c©Y e‡j|

(cvV 3 G ‡MvjKxq `c©Y m¤ú‡K© we¯ÍvwiZ Av‡jvPbv Kiv n‡q‡Q|)

9.2.2 †MvjKxq `c©Y (Spherical Mirror) GKwU †MvjK AvKvi e¯‘i c„ô hw` h‡_ó gm„Y nq Zv n‡j H c„‡ô AvcwZZ Av‡jvK iwk¥i wbqwgZ cÖwZdjb

N‡U| †MvjK c„ô cÖwZdjK ev `c©Y wnmv‡e e¨eüZ nq| ZvB, †h `c©‡Yi cÖwZdjK c„ô †Mvj‡Ki c„ô ev †MvjK

c„‡ôi Ask we‡kl Zv‡K †MvjKxq `c©Y e‡j|

Avgiv Rvwb GKwU †MvjK wb‡iU n‡Z cv‡i Avevi duvcvI n‡Z cv‡i| wb‡iU †Mvj‡Ki †Kej evB‡ii wcV ev DuPz

wcV cÖwZdjK wnmv‡e e¨envi n‡Z cv‡i| Ab¨ w`‡K †MvjKwU hw` duvcv nq Zv n‡j evB‡ii DuPz wcV A_ev

†fZ‡ii wbPz wcV A_©vr †h †Kv‡bv wcVB `c©Y wnmv‡e KvR K‡i| ZvB †MvjKxq `c©Y cÖavbZ `yÕ cÖKvi, DËj `c©Y

I AeZj `c©Y|

9.5 wP‡Î GKwU †fZ‡i duvcv †MvjK †`Lv‡bv n‡q‡Q| Gi †K›`ª

C| Gi GKwU Ask AB †K‡U wb‡q †fZ‡ii ev wbPz wc‡V cvi`

jvMv‡j evB‡ii ev DËj wcV `c©Y wnmv‡e KvR Ki‡e| GwU DËj

`c©Y|

Avevi Avi GKwU Ask A'B' †K‡U wb‡q Zvi evB‡ii ev DuPz wc‡V

cvi` jvMv‡j †fZ‡ii ev AeZj wcV `c©Y wnmv‡e KvR Ki‡e|

GwU AeZj `c©Y|

wPÎ t 9.5 AeZj I DËj `c©Y m„wó

AeZj `c©Y (Concave Mirror) t †Kv‡bv duvcv †Mvj‡Ki wfZ‡ii ev AeZj wc‡Vi wKQz Ask hw` gm„Y nq ev

cÖwZdjK iƒ‡c KvR K‡i Z‡e Zv‡K AeZj `c©Y e‡j|

DËj `c©Y (Convex Mirror) t †Kv‡bv duvcv ‡Mvj‡Ki evB‡ii ev DËj wc‡Vi wKQz Ask hw` gm„Y nq ev cÖwZdjK

iƒ‡c KvR K‡i Z‡e Zv‡K DËj `c©Y e‡j|

9.2.3 K‡qKwU msÁv (Some Definitions)

1. †giæ we›`y (Pole)t †MvjKxq `c©‡Yi cÖwZdjK c„‡ôi ga¨ we›`y ev †K› ª we›`y‡K `c©‡Yi †giæ we›`y ev ms‡ÿ‡c

†giæ e‡j| mvaviYZ DËj `c©‡Yi †ÿ‡Î cÖwZdjK c„‡ôi me‡P‡q DuPz we›`y Ges AeZj `c©‡Yi ‡ÿ‡Î

cÖwZdjK c„‡ôi me‡P‡q bxPz we›`yB †giæ we›`y| 9.6 Ges 9.7 bs wP‡Î P we› y¸‡jv `c©‡Yi †giæ|

2. eµZvi †K›`ª (Centre of Curvature)t †MvjKxq `c©Y †h †Mvj‡Ki Ask †mB †Mvj‡Ki †K›`ª‡K H `c©‡Yi

eµZvi †K› ª e‡j| 9.6 Ges 9.7 bs wP‡Î C eµZvi †K›`ª|

3. eµZvi e¨vmva© ( Radius of Curvature)t †MvjKxq `c©Y †h †Mvj‡Ki Ask †mB †Mvj‡Ki e¨vmva©‡K H `c©‡Yi

eµZvi e¨vmva© e‡j| 9.6 Ges 9.7 bs wP‡Î CP ev CP' ˆ`N© H `c©‡Yi eµZvi e¨vmva©| g~jZ eµZvi

†K›`ª †_‡K `c©‡Yi †giæ we›`y ch©šÍ `~iZ¡‡K H `c©‡Yi eµZvi e¨vmva© aiv nq| eµZvi e¨vmva©‡K mvaviYZ r Aÿi Øviv cÖKvk Kiv nq|

4. cÖavb Aÿ (Principal axis) t †MvjKxq `c©‡Yi †giæ Ges eµZvi †K‡›`ªi ga¨ w`‡q MgbKvix mij‡iLv‡K

`c©‡Yi cÖavb Aÿ e‡j| 9.6 Ges 9.7 bs wP‡Î CP mij‡iLv `c©‡Yi cÖavb Aÿ| cÖavb Aÿ‡K Dfq w`‡K

hZ `~i B”Qv ewa©Z Kiv hvq| ZLbI G‡K cÖavb AÿB e‡j| 9.8 bs wP‡Î APC ev ACP GBiƒc cÖavb Aÿ

†`Lv‡bv n‡q‡Q|

c`v_©weÁvb

BDwbU 9 c„ôv # 195

5. †MŠY Aÿ (Secondary axis)t †giæ we›`y e¨ZxZ `c©Y Z‡ji †h †Kv‡bv we›`y Ges `c©‡Yi eµZvi †K‡`ªi ga¨

w`‡q MgbKvix mKj mij‡iLv‡K ‡MŠY Aÿ e‡j| 9.6 Ges 9.7 bs wP‡Î CP' †MŠY Aÿ| cÖavb Aÿ Ges

†MŠY Aÿ Df‡qB `c©Y Z‡ji Dci j¤ nq|

wPÎ t 9.6 DËj `c©Y wPÎ t 9.7 AeZj `c©Y

6. cÖavb †dvKvm (Principal Focus) t AeZj `c©‡Y AvcwZZ cÖavb A‡ÿi wbKUeZx© Ges cÖavb A‡ÿi

mgvšÍivj Av‡jvK iwk¥ ¸”Q cÖwZdj‡bi ci cÖavb A‡ÿi Dci GKwU wbw`©ó we›`y‡Z ci¯úi‡K †Q` K‡i ev

wgwjZ nq| H we›`y‡K AeZj `c©‡Yi cÖavb †dvKvm e‡j| 9.8 (K) wP‡Î F we›`ywU AeZj `c©‡Yi cÖavb

†dvKvm|

9.8 (L) wP‡Î ‡`Lv hv‡”Q GKwU DËj `c©‡Yi Dci AvcwZZ cÖavb A‡ÿi wbKUeZx© Ges cÖavb A‡ÿi

mgvšÍivj GK¸”Q Av‡jvK iwk¥ cÖwZdj‡bi ci Pvwiw`‡K Qwo‡q co‡Q, wKš‘ g‡b n”Q cÖwZdwjZ iwk¥¸‡jv

cÖavb A‡ÿi Dci¯’ GKwU wbw`©ó we›`y F †_‡K Qwo‡q co‡Q ev Acm„Z n‡”Q| GB F we›`ywU AeZj MPM′ `c©‡Yi cÖavb †dvKvm|

†MvjKxq `c©‡Y AvcwZZ cÖavb A‡ÿi wbKUeZx© mgvšÍivj iwk¥¸”Q cÖwZdj‡bi ci cÖavb A‡ÿi Dci †h

we›`y‡Z wgwjZ nq (AeZj `c©‡Y) A_ev †h we›`y ‡_‡K Qwo‡q co‡Q ev Acm„Z n‡”Q e‡j g‡b nq (DËj

`c©‡Y) Zv‡K H `c©‡Yi cÖavb †dvKvm e‡j |

wPÎ t 9.8 (K) AeZj `c©‡Y cÖwZdjb

wPÎ t 9.8 (L) DËj `c©‡Y cÖwZdjb

7. †dvKvm `~iZ¡ (Focal length)t †MvjKxq `c©‡Yi †giæ †_‡K cÖavb †dvKvm we› y ch©šÍ `~iZ¡‡K Zvi †dvKvm

`~iZ¡ e‡j| 9.8 (K) I 9.8 (L) bs wP‡Î `ywU `c©‡Yi †dvKvm `~iZ¡ PF Avjv`v Avjv`v K‡i †`Lv‡bv n‡q‡Q|

mvaviYZ f Aÿi Øviv †dvKvm `~iZ¡ cÖKvk Kiv nq|

8. †dvKvm Zj (Focal plane)t †Kv‡bv †MvjKxq `c©‡Yi cÖavb †dvKv‡mi ga¨ w`‡q cÖavb A‡ÿi mv‡_ j¤fv‡e †h

mgZj Kíbv Kiv nq Zv‡K †dvKvm Zj e‡j| ZË¡xqfv‡e †dvKvm Zj Amxg ch©šÍ we¯Í…Z|

9. †MŠY †dvKvm (Secondary focus)t †MvjKxq `c©‡Y AvcwZZ mgvšÍivj iwk¥¸”Q cÖavb A‡ÿi mgvšÍivj bv n‡j

cÖwZdj‡bi ci cÖavb A‡ÿi evB‡i GKwU we›`y‡Z wgwjZ nq (AeZj `c©‡Y) A_ev GKwU we›`y ‡_‡K Qwo‡q

co‡Q ev Acm„Z n‡”Q e‡j g‡b nq (DËj `c©‡Y) H we›`y‡K `c©‡Yi †MŠY †dvKvm e‡j| GKwU ‡MvjKxq

`c©‡Yi cÖavb †dvKvm we›`y gvÎ GKwU; wKš‘ †MŠY ‡dvKvm AmsL¨| GB we›`y¸‡jv cÖavb A‡ÿi evB‡i wKš‘

†dvKvm Z‡j Ae¯’vb K‡i|

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 196

9.3.3 †MvjKxq `c©‡Yi †dvKvm ~iZ¡ I eµZvi e¨vmv‡a©i g‡a¨ m¤úK©

(Relation between Focal length and Radius of curvature of a spherical mirror) K. AeZj `c©‡Yi †ÿ‡Î t

9.9 wP‡Î MPM΄ GKwU AeZj `c©Y| Gi eµZvi †K›`ª C, †giæ we› y P, cªavb Aÿ CP, cÖavb †dvKvm F| aiv hvK cÖavb Aÿ CP Gi wbKUeZx© Ges

mgvšÍivj iwk¥ AQ `c©‡Yi Q we›`y‡Z AvcwZZ n‡q‡Q| QC †hvM Kiv n‡jv| QC `c©‡Yi eµZvi e¨vmva© e‡j GwU Q we›`y‡Z `c©Y Z‡j j¤| (e„‡Ëi †K›`ª

†_‡K cwiwai †h †Kvb we›`y ms‡hvMKvix †iLv e„‡Ëi cwiwai H we›`y‡Z j¤

nq)| Zvn‡j AQC AvcZb †KvY|

wPÎ 9.9

GLb cÖwZdj‡bi m~Î Abymv‡i AvcZb †KvY AQC Gi mgvb K‡i ‡KvY CQR A¼b Kiv hvK| †hb QR iwk¥ cÖavb

Aÿ CP †K F we› y‡Z †Q` K‡i|

msÁvbymv‡i CQR cÖwZdjb †KvY, QR cÖwZdwjZ iwk¥ Ges F AeZj `c©YwUi cÖavb †dvKvm| cÖwZdj‡bi

m~Îvbymv‡i AvcZb †KvY AQC = cÖwZdjb †KvY CQR|

Avevi AQ mgvšÍivj CP | QC ‡Q`K, AZGe AQC = GKvšÍi QCF CQF = QCF QCF mgwØevû| myZivs CF = QF GLb Q we›`y P we› yi Lye KvQvKvwQ nIqvq QF = FP = CF ev, CF = FP

AZGe F, CP Gi ga¨ we› y| myZivs PF = 12

CP

wKš‘ PF = †dvKvm ~iZ¡ = f Ges PC = eµZvi e¨vmva© = r

2rf A_©vr AeZj `c©‡Yi †dvKvm ~iZ¡ eµZvi e¨vmv‡a©i A‡a©K|

L. DËj `c©‡Yi †ÿ‡Î t

9.10 wP‡Î MPM΄GKwU DËj `c©Y| Gi eµZvi †K›`ª C, †giæ

we›`y P cªavb Aÿ CP, cÖavb †dvKvm, F| aiv hvK cÖavb Aÿ CP

Gi wbKUeZx© Ges mgvšÍivj iwk¥ AQ `c©‡Yi Q we›`y‡Z AvcwZZ

n‡q‡Q| CQ †hvM K‡i N ch©šÍ ewa©Z Kiv n‡jv| CQ `c©‡Yi

eµZvi e¨vmva© e‡j QN, Q we› y‡Z `c©Y Z‡j Awfj¤^| (e„‡Ëi

†K›`ª †_‡K cwiwai †h †Kvb we›`y ms‡hvMKvix †iLv e„‡Ëi cwiwai

H we›`y‡Z j¤ nq)| Zvn‡j AQN AvcZb †KvY|

wPÎ 9.10

GLb cÖwZdj‡bi m~Î Abymv‡i AvcZb †KvY AQN Gi mgvb K‡i †KvY NQR AsKb Kiv hvK †hb RQ iwk¥‡K

†cQ‡b ewa©Z Ki‡j Zv cÖavb Aÿ CP †K F we› y‡Z †Q` K‡i| msÁvbymv‡i NQR cÖwZdjb †KvY, QR cÖwZdwjZ iwk¥ Ges F AeZj `c©YwUi cÖavb †dvKvm we›`y| cÖwZdj‡bi

m~Îvbymv‡i AvcZb †KvY AQN = cÖwZdjb †KvY RQN|

Avevi AQ mgvšÍivj PC| NC †Q`K, AZGe NQA = Abyiƒc QCF Ges RQN = CQF ( wecÖZxc †KvY e‡j); CQF = QCF QCF mgwØevû| myZivs FC = FQ GLb Q we›`y P we› yi Lye KvQvKvwQ nIqvq FQ = FP = FC ev, CF = FP

c`v_©weÁvb

BDwbU 9 c„ôv # 197

AZGe F, CP Gi ga¨ we› y| myZivs PF = 12

PC

wKš‘ PF = †dvKvm ~iZ¡ = f Ges PC = eµZvi e¨vmva© = r

∴ 2rf A_©vr DËj `c©‡Yi †dvKvm `~iZ¡ eµZvi e¨vmv‡a©i A‡a©K|

myZivs †`Lv hvq me †ÿ‡ÎB †Mvjxq `c©‡Yi †dvKvm `~iZ¡ Zvi eµZvi e¨vmv‡a©i A‡a©K|

mvi-ms‡ÿc:

`c©Y t we‡klfv‡e cÖ ‘Z †h gm„Y Z‡j Av‡jvi wbqwgZ cÖwZdjb N‡U Zv‡K `c©Y e‡j| Kv‡Pi cv‡Zi GK wc‡V

avZzi cÖ‡jc jvwM‡q `c©Y ˆZwi Kiv nq| GB cÖ‡jc †`qv‡K cvi` jvMvb ev wmjfvwis ejv nq| `c©Y cÖavbZ

`yÕai‡Yi | h_v- mgZj `c©Y Ges †MvjKxq `c©Y|

cv‡VvËi g~j¨vqb -9.2

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| †KvbwU `c©Y wnmv‡e KvR K‡i?

(K) cvwjk Kiv †Uwej (L) cwi®‹vi cvi` c„ô

(M) w ’i cvwb c„ô (N) me¸‡jv

2| †Kvb ai‡Yi cÖwZdjK Z‡j wbqwgZ cÖwZdjb N‡U?

(K) eµZj `c©‡Y (L) mgZj `c©‡Y

(M) AeZj `c©‡Y (N) me ai‡Yi `c©‡Y

3| GKwU DËj `c©‡Yi eµZvi e¨vmva© 14 cm n‡j Gi †dvKvm `~iZ¡ KZ?

(K) 14 cm (L) 28 cm

(M) 7 cm (N) 3.5 cm

4| AeZj `c©‡Yi eµZvi e¨vmva© r Ges †dvKvm `~iZ¡ f n‡j †KvbwU mwVK?

(K) r = 2f (L) f = 2r

(M) r = f (N) f > r

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 198

cvV-3 mgZj `c©‡Y cÖwZwe¤ (Image Formed by Plane Mirror)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. mgZj `c©‡Y wKfv‡e cÖwZwe¤ MwVZ nq, Zv wP‡Îi mvnv‡h¨ e¨vL¨v Ki‡Z cvi‡eb|

2. mgZj `c©‡Y we¤ m„wó m¤ú‡K© K‡qKwU mvaviY NUbv eY©bv Ki‡Z cvi‡eb |

3. mgZj `c©‡Y MwVZ cÖwZwe‡¤i ˆewkó¨mg~n eY©bv Ki‡Z cvi‡eb |

9.3.1 mgZj `c©‡Y cÖwZwe¤ MVb (Formation of image by a plane mirror) e¯‘ hZ e„nr ev hZ ÿz`ªB †nvK bv †Kb `c©‡Yi mvg‡b ivL‡j `c©‡Yi †cQ‡b Zvi cÖwZwe¤ MwVZ nq|

iwk¥i †iLv wP‡Îi gva¨‡g Avgiv e¯‘ †_‡K MwVZ we‡¤i Ae¯’vb I AvKvi AvK…wZ wbiƒcb Ki‡Z cvwi|

Avgiv GKwU we›`y e¯‘ Ges GKwU we¯Í…Z e¯‘i cÖwZwe¤ MV‡bi cÖwµqv I MwVZ cÖwZwe‡¤i Ae¯’vb I AvKvi AvK…wZ

eY©bv Kie|

(K) we›`y jÿ¨e ‘ Øviv cÖwZwe¤ MVb

aiv hvK GKwU mgZj `c©Y M1 M2 Gi mvg‡b O GKwU we›`y jÿ¨e ‘ (wPÎ 9.11)| jÿ¨e ‘ (O we› y) †_‡K me

w`‡K Av‡jvK iwk¥ Qwo‡q co‡Q| Zvi g‡a¨ †ek wKQz iwk¥ `c©Y Z‡j co‡Q| Gi GKwU iwk¥ OP eivei `c©Y

Z‡j P we› y‡Z AvcwZZ n‡q PR c‡_ cÖwZdwjZ n‡q `k©‡Ki †PvL co‡Q| Avi GKwU iwk¥ OQ, M1M2 `c©Y Z‡j

Q we› y‡Z AvcwZZ n‡q QS c‡_ cÖwZdwjZ n‡q `k©‡Ki †Pv‡L co‡Q|

wPÎ t 9.11 we› y jÿ¨e ‘i cÖwZwe¤ MVb

†Pv‡L cÖ‡ekKvix cÖwZdwjZ PR Ges QS iwk¥ `yÕwU †cQ‡b

ewa©Z Ki‡j I we›`y‡Z wgwjZ nq| g‡b nq I we›`y †_‡K

mivmwi iwk¥ `yÕwU †Pv‡L G‡m co‡Q| I we›`y‡Z jÿ¨e¯‘ O

we›`yi cÖwZ”Qwe ˆZwi nq|

cÖwZwe¤wU †`Lv hvq, wKš‘ aiv ev †Qvuqv hvq bv| GgbwK

c`©vi DciI †djv hvq bv| ZvB GwU GKwU Am` ev

Aev¯Íe cÖwZwe¤| mgZj `c©‡Y me mgq Am` cÖwZwe¤

MwVZ nq|

9.11 wP‡Î P I Q we›`y‡Z `c©Y Z‡ji Ici PN1 Ges QN2 Awfj¤| OI †hvM Ki‡j `c©Y Zj‡K M we›`y‡Z †Q`

Kij|

cÖwZdj‡bi wbqg Abyhvqx, OPN1 = RPN1

OI mgvšÍivj PN1 †h‡nZz Df‡qB M1M2 `c©Y Z‡j Awfj¤|

AZGe hLb OP †Q`K OPN1 = POM (GKvšÍi †KvY e‡j)

Avevi hLb OP †Q`K RPN1 = PIM ( Abyiƒc †Kvb e‡j)

∴ POM = PIM (∵OPN1 = RPN1) GLb, ∆OPM Ges ∆IPM Gi g‡a¨ IMP = OMP ( ∵ cÖ‡Z¨‡K mg‡KvY)

POM = PIM Ges PM mvaviY evû| myZivs ∆ ywU me©mg| ∴ OM = IM ev, `c©Y †_‡K e ‘i `~iZ¡ = `c©Y †_‡K we‡¤i ~iZ¡|

ms‡ÿ‡c, e¯‘ ~iZ¡ = cÖwZwe¤ `~iZ¡|

c`v_©weÁvb

BDwbU 9 c„ôv # 199

(L) we¯Í…Z e¯‘i cÖwZwe¤ MVb

9.11 wP‡Î Avgiv GKwU we›`y‡K jÿ¨e¯‘ we‡ePbv K‡iwQ| cÖK…Z c‡ÿ we›`y e¯‘ m¤¢e bq| me e¯‘iB wbw`©ó AvKvi-

AvK…wZ Av‡Q| A_©vr e¯‘ g~jZ we¯Í…Z| Z‡e mKj we Í…Z e¯‘B AmsL¨ we›`y e¯‘i mgwó| GB we›`y¸‡jvi cÖwZwe¤

†MvUv e¯‘i cÖwZwe¤ MVb K‡i| wKš‘ †Kvb we¯Í…Z e¯‘i cÖwZwe¤ MV‡bi wPÎ †c‡Z n‡j Gi cÖwZwU we›`yi cÖwZwe‡¤i

wPÎ AvuKv cÖ‡qvRb nq bv| we‡kl K‡qKwU we›`yi cÖwZwe¤ MV‡bi wPÎ AvuK‡Z nq| GKwU D`vniY jÿ¨ Kiæb|

M M′ `c©Y Z‡ji mvg‡b AO GKwU we¯Í…Z e¯‘ (wPÎ 9.12)| Gi kxl© we›`y O †_‡K `yÕwU iwk¥ OP Ges OP′ `c©Y

Z‡j AvcwZZ n‡q cÖwZdj‡bi wbqg Abyhvqx cÖwZdwjZ nq| cÖwZdwjZ iwk¥ `yÕwU Gu‡K †cQ‡b ewa©Z Kiv n‡q‡Q|

9.12 wP‡Î †`Lv‡bv n‡q‡Q Giv I we› y‡Z wgwjZ n‡q‡Q| I we›`y‡Z O we› yi cÖwZwe¤ m„wó n‡q‡Q|

GKB fv‡e e¯‘wUi cv`we›`y A †_‡K `yÕwU iwk¥ AQ Ges AQ′ `c©Y

Z‡j AvcwZZ n‡q †h c‡_ cÖwZdwjZ n‡e Zvi †iLv wPÎ Gu‡K

†cQ‡b evov‡j GKwU we›`y‡Z wgwjZ n‡q‡Q (wP‡Î B we›`y †`Lv‡bv

n‡q‡Q)| GB we›`y‡Z A_©vr B we›`y‡Z A we›`yi cÖwZwe¤ m„wó n‡e|

Gevi I Ges B we›`y `'ywU mshy³ Ki‡j †h we¯Í…Z mij †iLv IB

cvIqv hv‡e GUvB OA e¯‘i cÖwZwe¤ (wPÎ 9.12)| GwUI Am`

cÖwZwe¤| GwU AvK…wZ Ges AvKv‡i AO e¯‘i mgvb| Ges e¯‘

†_‡K `c©‡Yi `~iZ¡ hZ `c©Y †_‡K cÖwZwe‡¤i ~iZ¡I ZZ|

wPÎ t 9.12 we Í…Z jÿ¨e ‘i cÖwZwe¤ MVb

9.3.2 mgZj `c©‡Y we¤ m„wó m¤ú‡K© K‡qKwU mvaviY Z_¨

Some commone facts about image formation by plane mirror

(K) mgZj `c©‡Y wb‡Ri c~Y© cÖwZwe¤ †`L‡Z n‡j `c©‡Yi ˆ`N© `k©‡Ki ˆ`‡N©¨i b~¨bZg A‡a©K n‡Z n‡e

9.13 wP‡Î Lvovfv‡e ¯’vwcZ MM′ GKwU mgZj `c©‡Yi mvg‡b HEF GKRb `k©K| `k©‡Ki gv_v †PvL Ges cv

h_vµ‡g H, E Ges F we› y w`‡q †`Lv‡bv n‡q‡Q| `k©K ZLbB Zvi m¤ú~Y© cÖwZwe¤ †`L‡Z cv‡eb hLb Zvi gv_v H

Ges cv F †_‡K `c©‡Y AvcwZZ Av‡jvK iwk¥ cÖwZdj‡bi ci Zvi †Pv‡L E we› y‡Z co‡Z n‡e| aiv hvK MwVZ

cÖwZwe¤wU‡Z gv_v H1 Ges cv F1|

m~Î Abymv‡i MwVZ cÖwZwe‡¤^i ˆ`N© = e¯‘i ˆ`N© Ges cÖwZe‡¤i ~iZ¡ = e¯‘i `~iZ¡

A_©vr, HF = H1 F1 ; FM′ = F1M′ Ges HM = H1M (wP‡Î H, H1 Ges F, F1 ms‡hvMKvix †iLv `ywU `c©YZj‡K h_vµ‡g M Ges M′ we› y‡Z j¤fv‡e †Q` K‡i‡Q)|

wPÎ t 9.13 mgZj `c©‡Y wb‡Ri c~Y© cÖwZwe¤ `k©b

Gevi E F1 Ges E H1 †hvM Kiv n‡jv †hb G¸‡jv

`c©YZj‡K h_vµ‡g Q Ges P we› y‡Z †Q` K‡i| HP Ges FQ †hvM Kiv n‡jv| `k©‡Ki m‡e©v”P we›`y H †_‡K

`c©‡Yi P we›`y‡Z AvcwZZ iwk¥ cÖwZdwjZ n‡q `k©‡Ki

†Pv‡L E we›`y‡Z cÖ‡ek Ki‡Q Ges H1 we›`y‡Z cÖwZwe¤

MVb Ki‡Q| Abyiƒcfv‡e `k©‡Ki me©wbgœ we›`y F †_‡K

`c©‡Yi Q we›`y‡Z AvcwZZ iwk¥ cÖwZdwjZ n‡q `k©‡Ki

†Pv‡L E we›`y‡Z cÖ‡ek Ki‡Q Ges F1 we›`y‡Z cÖwZwe¤

MVb Ki‡Q|

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 200

myZivs HF `k©‡Ki c~Y© cÖwZwe¤^ H1 F1 †`L‡Z n‡j `c©‡Yi ˆ`N¨© Kgc‡ÿ PQ nIqv cÖ‡qvRb|

GLb, wP‡Î H1EF1 wÎfz‡Ri f‚wg H1F1 Ges PQ, H1F1 Gi mgvšÍivj| (†h‡nZz PQ `c©Y Zj MM′ Gi Ask)|

AZGe PQ =21

H1F1 ev, `c©‡Yi ˆ`N© =

21

× `k©‡Ki ˆ`N¨©

A_©vr, mgZj `c©‡Y wb‡Ri c~Y© cÖwZwe¤ †`L‡Z n‡j `c©‡Yi ˆ`N© `k©‡Ki ˆ`‡N© i b~¨bZg A‡a©K n‡Z n‡e|

(L) mgZj `c©‡Y cÖwZwe‡¤i cvk¦© cwieZ©b nq (Lateral inversion in plane mirror)

mgZj `c©‡Yi mvg‡b `uvwo‡q `k©K Wvb nvZ Zzj‡j `c©‡Yi g‡a¨ Zvi cÖwZwe¤wU evg nvZ Zzj‡e| `k©K evg nvZ

bvo‡j cÖwZwe‡¤i Wvb nvZ bo‡e| g‡b nq mgMÖ †`‡ni evg cvk¦© cwieZ©b n‡q Wvb cv‡k¦© Ges Wvb cvk¦© evg cv‡k¦©

P‡j †M‡Q| G‡K ejv nq cÖwZwe‡¤i cvk¦© cwieZ©b| mgZj `c©‡Y m„ó cÖwZwe¤ ~iZ¡ Ges jÿ¨e¯‘i `~iZ¡ mgvb

nIqvi Rb¨ GiKg nq|

GK UzK‡iv KvM‡R K Aÿi wj‡L GKwU mgZj `c©‡Yi mvg‡b

ai‡j †`Lv hv‡e cÖwZwe¤wU D‡ë †M‡Q (wPÎ 9.14)| Z‡e

cÖwZmg e¯‘mg~‡ni cvk©¦ cwieZ©b †evSv hvq bv| †hgb 0, 4,| +

= ai‡bi wPnè ev AvK…wZi cvk©¦ cwieZ©b eySv hvq bv| Avgiv

†Wªwms †Uwe‡ji ev †mjy‡bi Avqbvq wb‡R‡`i †h cÖwZwe¤ †`wL

Zvi cvk¦© cwieZ©b ÎæwU hy³|

wPÎ t 9.14 mgZj `c©‡Y we‡¤i cvk¦© cwieZ©b

(M) mgZj `c©‡Y cici yevi cÖwZdj‡bi mij †cwi‡¯‹vc (Simple Periscope)

wPÎ t 9.15 mij †cwi‡¯‹vc w`‡q fxo

Gwo‡q †Ljv †`Lv

e¯‘ †_‡K AvMZ iwk¥i cici

`yevi mgZj `c©‡Y cÖwZdj‡bi

d‡j MwVZ cÖwZwe¤ †`Lvi GKwU

mnR hš¿ †cwi‡¯‹vc|

GwU GKwU j¤v AvqZvKvi Kv‡Vi ev avZzi ˆZwi j¤v bj| GB h‡š¿i

b‡ji g‡a¨ `ywU mgZj `c©Y‡K c¯ú‡ii gy‡LvgywL Ges mgvšÍivj K‡i

b‡ji A‡ÿi mv‡_ 45º †Kv‡Y emv‡bv nq|

9.15 wP‡Î GKwU mij †cwi‡¯‹vc †`Lv‡bv n‡q‡Q| `~‡ii e¯‘ †_‡K

Av‡jvK iwk¥ cª_‡g †mvRv G‡m M1 `c©‡Y AvcwZZ nq| AvcwZZ

iwk¥ cÖwZdwjZ n‡q b‡ji Aÿ eivei G‡m M2 `c©‡Y c‡o Ges M2

`c©‡Y cybivq cÖwZdwjZ n‡q Avbyf~wgK fv‡e `k©‡Ki †Pv‡L c‡o d‡j

jÿ¨e¯‘ †`Lv hvq| G‡ÿ‡Î `yevi cÖwZdj‡bi Rb¨ jÿe¯‘i cvk¦©

cwieZ©‡bi ÎæwU ev cvk¦© cwieZ©b RwbZ mgm¨v _v‡K bv| ~‡ii ev

Kv‡Qi wRwbm †mvRvmywR †`L‡Z evav _vK‡j GB hš¿ e¨envi Kiv nq|

fxo Gwo‡q †Ljv †`Lv, Wy‡ev Rvnv‡R e‡m mgy`ªc„‡ô kÎæ c‡ÿi

Rvnv‡Ri MwZwewa ch©‡eÿY Kiv I †m g‡Zv Kv‡R e¨eüZ nq|

c`v_©weÁvb

BDwbU 9 c„ôv # 201

9.3.4 mgZj `c©‡Y MwVZ cÖwZwe‡¤i ˆewkó¨mg~n (Properties of image in plane mirror) mgZj `c©‡Y m„ó we‡¤i KZ¸‡jv ˆewkó¨ i‡q‡Q| †m¸‡jv n‡jv t

1. `c©Y †_‡K e ‘ ~iZ¡ hZ, `c©Y †_‡K we‡¤i `~iZ¡ ZZ|

2. e¯‘ I we¤ ms‡hvMKvix †iLv `c©Y Zj‡K j¤fv‡e †Q` K‡i|

3. mgZj `c©‡Y MwVZ we¤ Am` I †mvRv|

4. we‡¤i AvKvi e¯‘i AvKv‡ii mgvb nq|

5. we‡¤i cvk¦© cwieZ©b N‡U|

mvi-ms‡ÿc:

AeZj `c©Y t †Kvb duvcv ‡Mvj‡Ki wfZ‡ii ev AeZj wc‡Vi wKQz Ask hw` gm„Y nq ev cÖwZdjK iƒ‡c KvR K‡i

Z‡e Zv‡K AeZj `c©Y e‡j|

DËj `c©Y t †Kvb duvcv ‡Mvj‡Ki evB‡ii ev DËj wc‡Vi wKQz Ask hw` gm„Y nq ev cÖwZdjK iƒ‡c KvR K‡i Z‡e

Zv‡K DËj `c©Y e‡j|

†giæ we›`y t †MvjKxq `c©‡Yi cÖwZdjK c„‡ôi ga¨ we›`y ev †K›`ª we› y‡K `c©‡Yi †giæ e‡j|

eµZvi †K› ª t †MvjKxq `c©Y †h †Mvj‡Ki Ask †mB †Mvj‡Ki †K› ª‡K Zvi eµZvi †K› ª e‡j|

eµZvi e¨vmva© t †MvjKxq `c©Y †h †Mvj‡Ki Ask †mB †Mvj‡Ki e¨vmva©‡K H `c©‡Yi eµZvi e¨vmva© e‡j|

cÖavb Aÿ t †MvjKxq `c©‡Yi †giæ Ges eµZvi †K‡›`ªi ga¨ w`‡q MgbKvix mij‡iLv‡K `c©‡Yi cÖavb Aÿ e‡j|

cv‡VvËi g~j¨vqb -9.3

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| mgZj `c©‡Y `k©‡Ki c~Y© cÖwZwe¤ †`L‡Z n‡j `c©‡Yi ˆ`N© `k©‡Ki D”PZvi KZ n‡e?

(K) mgvb (L) eo

(M) Kg c‡ÿ A‡a©K (N) †h †Kv‡bv gv‡ci

2| †Kvb e ‘i †ÿ‡Î cvk¦© cwieZ©b nq bv?

(K) †h †Kv‡bv Nb e ‘‘ (L) †h †Kv‡bv gvbyl

(M) AcÖwZmg e¯‘ (N) cÖwZmg e¯‘

cvV-4 †MvjKxq `c©‡Y cÖwZwe¤ (Immage formed by Spherical Morror)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. †MvjKxq `c©‡Y cÖwZwe¤ MV‡bi iwk¥ wPÎ AuvK‡Z cvi‡eb|

2. AeZj `c©‡Y ev Íe cÖwZwe¤ m„wó e¨vL¨v Ki‡Z cvi‡eb|

3. AeZj `c©‡Y ev Íe Aev¯Íe cÖwZwe¤ m„wó e¨vL¨v Ki‡Z cvi‡eb|

4. DËj `c©‡Y e¯‘i cÖwZwe¤ m„wó e¨vL¨v Ki‡Z cvi‡eb|

5. †MvjKxq `c©‡Y m„ó cÖwZwe‡¤i ˆewkó¨ eY©bv Ki‡Z cvi‡eb|

9.4.1 †MvjKxq `c©‡Y cÖwZwe¤ MV‡bi e¨vLvi Rb¨ K‡qKwU iwk¥i c_‡iLv

(Ray Diagram of Spherical Mirror for explaining formation of Image) DËj ev AeZj `c©‡Yi mvg‡b †Kv‡bv e¯‘ ivL‡j `c©‡Y Zvi cÖwZwe¤ MwVZ nq| GB we‡¤^i Ae¯’vb,

AvKvi I cÖK…wZ Rvb‡Z n‡j iwk¥ wPÎ AvuK‡Z nq| e¯‘ †_‡K wbtm„Z ev wbM©Z iwk¥¸”Q `c©‡Y cÖwZdwjZ n‡q

†Kv_vq wgwjZ nq ev †Kv_v †_‡K wbtm„Z n‡”Q e‡j g‡b nq iwk¥ wP‡Îi gva¨‡g Zv Rvbv hvq| G iwk¥ wPÎ MV‡bi

Rb¨ `c©‡Yi cÖavb Aÿ, cÖavb †dvKvm, eµZvi †K›`ª Ges †giæ we›`y wbw`©ó _vK‡j K‡qKwU we‡kl AvcwZZ iwk¥i

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 202

cÖwZdjb ev cÖwZmi‡Yi c_‡iLv AbymiY Ki‡j KvRwU mnR nq| 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 `c©‡Yi †ÿ‡Î mPivPi

wb‡Pi wZb ai‡Yi iwk¥I †h †Kv‡bv `ywU we‡ePbv Kiv hvq| G¸‡jv n‡jv,-

1. †MvjKxq `c©‡Yi eµZvi e¨vmva© eivei AvcwZZ iwk¥

2. †MvjKxq `c©‡Yi cÖavb A‡ÿi mv‡_ mgvšÍivjfv‡e AvcwZZ iwk¥

3. †MvjKxq `c©‡Yi cÖavb †dvKv‡mi ga¨ w`‡q ev cÖavb †dvKvm eivei AvcwZZ iwk¥

†MvjKxq `c©‡Yi eµZvi e¨vmva© eivei AvcwZZ iwk¥ t

†MvjKxq `c©‡Yi eµZvi e¨vmva© eivei AvcwZZ iwk¥ g~jZt j¤fv‡e `c©‡Yi Dci c‡o, ZvB cÖwZdj‡bi

wbqgvbymv‡i GB iwk¥ cÖwZdj‡bi ci Avevi †mB c‡_B wd‡i hv‡e (wPÎ- 9.16 Ges wPÎ-9.17)|

wPÎ t 9. 16 AeZj `c©‡Y eµZvi e¨vmva© eivei

AvcwZZ iwk¥

wPÎ t 9.17 DËj `c©‡Y eµZvi e¨vmva© eivei

AvcwZZ iwk¥

9.16 wP‡Î MM © AeZj `c©‡Yi Dci Ges 9.17 wP‡Î MM © DËj `c©‡Yi Dci GKwU iwk¥ AQ, `c©‡Yi eµZvi

e¨vmva© CQ eivei Q we›`y‡Z j¤fv‡e AvcwZZ n‡q‡Q| AZGe cÖ_g iwk¥wU QCA c‡_ (9.16 wP‡Î) Ges wØZxq

iwk¥wU CQA c‡_ (9.17 wP‡Î) cÖwZdwjZ n‡e|

†MvjKxq `c©‡Yi cÖavb A‡ÿi mv‡_ mgvšÍivj fv‡e AvcwZZ iwk¥

cÖavb A‡ÿi mgvšÍivj AvcwZZ Av‡jvK iwk¥ AeZj `c©‡Y cÖwZdj‡bi ci cÖavb †dvKvm w`‡q hvq (wPÎ 9.18)|

DËj `c©‡Yi †ÿ‡Î cÖavb †dvKvm †_‡K Avm‡Q e‡j g‡b nq wPÎ (9.19)|

wPÎ 9.18 AeZj `c©‡Y cÖavb A‡ÿi mgvšÍiv‡j

AvcwZZ iwk¥

wPÎ 9.19 DËj `c©‡Y cÖavb A‡ÿi mgvšÍiv‡j

AvcwZZ iwk¥

9.18 bs wP‡Î GKwU iwk¥ AQ AeZj `c©‡Yi cÖavb Aÿ CP Gi mgvšÍivj n‡q Q we›`y‡Z AvcwZZ n‡q cÖavb

†dvKvm F w`‡q QR c‡_ cÖwZdwjZ nq| 9.19 bs wP‡Î GKwU iwk¥ AQ DËj `c©‡Yi cÖavb Aÿ PC Gi mgvšÍiv‡j

Q we› y‡Z AvcwZZ n‡q QR c‡_ cÖwZdwjZ nq, g‡b nq †hb GwU cÖavb †dvKvm F †_‡K Avm‡Q|

†MvjKxq `c©‡Yi cÖavb †dvKv‡mi ga¨ w`‡q ev cÖavb †dvKvm eivei AvcwZZ iwk¥

cÖavb †dvKv‡mi ga¨ w`‡q AeZj `c©‡Y AvcwZZ Av‡jvK iwk¥ Ges DËj `c©‡Y cÖavb †dvKvm eivei AvcwZZ

iwk¥ DfqwUB cÖwZdj‡bi ci cÖavb A‡ÿi mgšÍivj nq|

c`v_©weÁvb

BDwbU 9 c„ôv # 203

wPÎ t 9.20 AeZj `c©‡Y cÖavb †dvKv‡mi ga¨

w`‡q AvcwZZ iwk¥

wPÎ t 9.21 DËj `c©‡Y cÖavb †dvKvm eivei

AvcwZZ iwk¥

9.20 bs wP‡Î GKwU iwk¥ AQ AeZj `c©‡Yi cÖavb †dvKvm F Gi ga¨ w`‡q `c©‡Yi Q we›`y‡Z AvcwZZ n‡q cÖavb

Aÿ PC Gi mgvšÍivj n‡q QR c‡_ cÖwZdwjZ n‡q‡Q| 9.21 bs wP‡Î GKwU iwk¥ AQ DËj `c©‡Yi cÖavb

†dvKvm F eivei Q we› y‡Z AvcwZZ n‡q cÖavb Aÿ CP Gi mgvšÍiv‡j QR c‡_ cÖwZdwjZ n‡q‡Q|

9.4.2 †MvjKxq `c©‡Y e¯‘i cÖwZwe¤ MV‡bi iwk¥ wPÎ

(Ray diagram of image formed by spherical mirror) †MvjKxq `c©‡Yi mvg‡b e¯‘ ivL‡j `c©‡Y cÖwZwe¤ MwVZ nq| Avgiv Rvwb, †Kv‡bv we›`y †_‡K wbtm„Z Av‡jvK

iwk¥¸”Q cÖwZdj‡bi ci hw` wØZxq †Kv‡bv we›`y‡Z wgwjZ nq ev wØZxq †Kv‡bv 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| GB bxwZi Dci wfwË K‡iB †MvjKxq `c©‡Yi Øviv MwVZ

we›`y e ‘ ev we¯Í…Z e ‘i MwVZ cÖwZwe‡¤^i iwk¥ wPÎ AvuKv nq|

†MvjKxq `c©‡Y we›`y jÿ¨e ‘i cÖwZwe¤ MVb

wb‡Pi wPÎmn AeZj I DËj Dfq cÖKvi `c©‡Yi Avjv`v Avjv`vfv‡e we›`y jÿ¨e¯‘ Øviv m„ó cÖwZwe‡¤i MVb eY©bv

I e¨vL¨v Kiv nj|

K. AeZj `c©‡Y we›`y jÿ¨e ‘i cÖwZwe¤ MVb

9.22 bs wP‡Î GKwU AeZj `c©Y MM Gi mvg‡b GKwU we›`y e ‘ O ivLv n‡q‡Q| aiv hvK O †_‡K cÖavb

A‡ÿi mgvšÍiv‡j GKwU iwk¥ OQ, `c©‡Yi Q we›`y‡Z AvcwZZ nj| cÖwZdj‡bi wbqg Abymv‡i GwU cÖavb †dvKvm

F Gi ga¨ w`‡q QFA c‡_ cÖwZdwjZ n‡e| O †_‡K Avi GKwU iwk¥ eµZvi †K›`ª C eivei OC c‡_ `c©‡Yi

Dci M΄ we›`y‡Z AvcwZZ n‡jv| iwk¥wU †h‡nZz j¤fv‡e AvcwZZ n‡q‡Q ZvB cÖwZdj‡bi wbqg Abymv‡i M΄CO c‡_ wd‡i hv‡e| QFA Ges M΄CO cÖwZdwjZ iwk¥ `yÕwU I we›`y‡Z †Q` Kij| I we›`y‡Z O we›`yi ev¯Íe cÖwZwe¤

MwVZ n‡e (wPÎ 9.22)|

wPÎ t 9.22 AeZj `c©‡Y we›`y jÿ¨e¯‘i cÖwZwe¤

MVb

wPÎ t 9.23 DËj `c©‡Y we›`y jÿ¨e ‘i

cÖwZwe¤ MVb

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 204

L. DËj `c©‡Y we›`y jÿ¨e¯‘i cÖwZwe¤

9.23 bs wP‡Î GKwU DËj `c©Y MM΄ Gi mvg‡b O we›`y‡Z GKwU we›`y e¯‘ O ivLv n‡q‡Q| aiv hvK O †_‡K

cÖavb A‡ÿi mgvšÍiv‡j GKwU iwk¥ OQ `c©‡Yi Q we›`y‡Z AvcwZZ n‡jv| cÖwZdj‡bi wbqg Abymv‡i GwU cÖavb

†dvKvm F eivei QS c‡_ cÖwZdwjZ n‡e| O †_‡K Avi GKwU iwk¥ eµZvi †K›`ª C eivei OC c‡_ `c©‡Yi

Dci R we›`y‡Z AvcwZZ n‡jv| iwk¥wU †h‡nZz j¤fv‡e AvcwZZ n‡q‡Q ZvB cÖwZdj‡bi wbqg Abymv‡i RO c‡_B

wd‡i hv‡e| g‡b n‡e iwk¥wU C we›`y †_‡K Avm‡Q| QS Ges RO cÖwZdwjZ iwk¥ `yÕwU ci¯úi Acmvix, G‡`i

†cQ‡b ewa©Z Ki‡j I we›`y‡Z †Q` Ki‡e| g‡b n‡e I we›`y †_‡K iwk¥ `yÕwU wbtm„Z n‡”Q| A_©vr I we›`y‡Z O we›`yi

cÖwZwe¤ MwVZ n‡e|

†MvjKxq `c©‡Y we¯Í…Z jÿ¨e ‘i cÖwZwe¤ MVb

†Kv‡bv we¯Í…Z e¯‘ g~jZt AmsL¨ we›`y e¯‘i mgwó| ZvB †Kv‡bv we¯‘„Z e¯‘i cÖwZwe¤ MV‡bi Rb¨ K‡qKwU (Kgc‡ÿ

2wU) we›`yi we‡¤i Ae¯’vb wbY©q Ki‡Z nq| c‡i GKwU mij‡iLv Øviv we›`y cÖwZwe¤ `yÕwU †hvM K‡i w`‡j mgMÖ

e¯‘wUi cÖwZwe‡¤i wPÎ cvIqv hvq| wb‡¤œ AeZj Ges DËj `c©‡Y we¯Í…Z e¯‘i cÖwZwe¤ MVb cÖwµqv eY©bv Kiv

n‡jv|

M. AeZj `c©‡Y we¯Í…Z jÿ¨ e ‘i ev¯Íe cÖwZwe¤ MVb

9.24 bs wP‡Î MM′ GKwU AeZj `c©Y †`Lv‡bv n‡q‡Q| P Gi †giæ, C eµZvi †K› ª, F cÖavb †dvKvm Ges PC

cÖavb Aÿ| `c©YwUi mvg‡b cÖavb A‡ÿi Ici A we›`y‡Z j¤fv‡e ’vwcZ AO GKwU jÿ¨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 cÖwZwe‡¤i

Ae¯’vb wbY©q K‡i, 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‡ÿi mgvšÍivj OQ iwk¥ AvuKv n‡jv hv cÖwZdj‡bi ci

cÖavb †dvKvm F we› y w`‡q hv‡e| O we› y †_‡K Avi GKwU iwk¥ eµZvi †K› ª C we› yi ga¨ w`‡q `c©YZ‡j M′ we›`y‡Z AvcwZZ n‡q M′CO c‡_ cÖwZdwjZ n‡e| QF I M′O cÖwZdwjZ iwk¥ `yÕwU I we›`y‡Z †Q` Ki‡e| I we›`y‡Z O we› yi cÖwZwe¤ MwVZ n‡e|

A †_‡K cÖavb Aÿ eivei AvcwZZ Av‡jvK iwk¥ cÖwZdj‡bi ci cÖavb A‡ÿi

Dci w`‡qB PA c‡_ cÖwZdwjZ n‡e| d‡j A we›`yi cÖwZwe¤ Aek¨B cÖavb

A‡ÿi Ici _vK‡e| Avevi †h‡nZz AO jÿ¨e¯‘wU cÖavb A‡ÿi Ici j¤,

†m‡nZz cÖwZwe¤wUI cÖavb A‡ÿi Ici j¤^ n‡e| ZvB I we›`y †_‡K cÖavb

A‡ÿi Ici IB j¤ Uvb‡j IB n‡e AO jÿ¨e¯‘i cÖwZwe¤^| 9.24 wPÎ †_‡K

†`Lv hvq cÖwZwe¤wU m`, D‡ëv Ges AvKv‡i jÿ¨e¯‘ †_‡K †QvU|

wPÎ 9.24 AeZj `c©‡Y we¯Í…Z

jÿ¨e¯‘i cÖwZwe¤ MVb

N. AeZj `c©‡Y we¯Í…Z jÿ¨ e ‘i Aev¯Íe cÖwZwe¤ MVb

9.25 wP‡Î MM GKwU AeZj `c©Y †`Lv‡bv n‡q‡Q| P Gi †giæ, C eµZvi †K›`ª, F cÖavb †dvKvm Ges PC

cÖavb Aÿ| `c©YwUi mvg‡b cÖavb A‡ÿi Dci A we›`y‡Z j¤fv‡e ’vwcZ AO GKwU jÿ¨e¯‘| OA e¯‘wU AmsL¨

we›`yi mgwó, hvi cÖvšÍ we›`y `ywU h_vµ‡g O(kxl©) Ges A (cv`we›`y)| GLb A Ges O we›`yi cÖwZwe‡¤i Ae¯’vb

wbY©q K‡i, 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‡ÿi mgvšÍivj OQ iwk¥ AvuKv n‡jv hv cÖwZdj‡bi ci

cÖavb †dvKvm F we› y w`‡q hv‡e| O we›`y †_‡K Avi GKwU

iwk¥ `c©YZ‡j M we›`‡Z AvcwZZ n‡q MOC c‡_ cÖwZdwjZ

n‡e| OQ Ges OM iwk¥ `ywU cÖwZdj‡bi ci Acmvix

iwk¥¸‡”Q cwiYZ n‡e| G‡`i‡K wcQb w`‡K evov‡j I we›`y

†_‡K Acm„Z n‡”Q e‡j g‡b n‡e| I †_‡K cÖavb A‡ÿi Dci

wPÎ : 9.25

M

I

B P A

O

F C

Q

M´

c`v_©weÁvb

BDwbU 9 c„ôv # 205

Aw¼Z IB j¤B n‡e AO jÿ¨e¯‘i cÖwZwe¤| 9.25 wPÎ †_‡K †`Lv hvq cÖwZwe¤wU Aev¯Íe, †mvRv Ges AvKv‡i

jÿ¨e¯‘ †_‡K eo|

O. DËj `c©‡Y we¯Í……Z e ‘i cÖwZwe¤ MVb

9.26 bs wP‡Î MM′ GKwU DËj `c©Y| P Gi †giæ, C eµZvi †K›`ª, F cÖavb †dvKvm Ges PC cÖavb Aÿ|

`c©YwUi mvg‡b cÖavb A‡ÿi Ici A we›`y‡Z j¤fv‡e ¯’vwcZ AO GKwU we¯Í…Z jÿ¨e¯‘| OA e¯‘wUi cÖwZwe¤

MV‡bi wPÎ AvuK‡Z n‡e|

O we›`y †_‡K cÖavb A‡ÿi mgvšÍivj OQ AvcwZZ iwk¥ Ges

Gi cÖwZdwjZ iwk¥ QS 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¥ OR

eµZvi †K› ª C we› yi eivei AvcwZZ n‡q RO c‡_

cÖwZdwjZ 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 9.26)| wPÎ t 9.26 DËj `c©‡Y we¯Í…Z jÿ¨e ‘i

cÖwZwe¤ MVb

A †_‡K cÖavb Aÿ eivei AvcwZZ Av‡jvK iwk¥ cÖwZdj‡bi ci cÖavb A‡ÿi Dci w`‡qB PA c‡_ cÖwZdwjZ

n‡e| d‡j A we›`yi cÖwZwe¤ Aek¨B cÖavb A‡ÿi Ici _vK‡e| Avevi †h‡nZz AO jÿ¨e¯‘wU cÖavb A‡ÿi Ici

j¤, †m‡nZz cÖwZwe¤wUI cÖavb A‡ÿi Ici j¤ n‡e| ZvB I we›`y †_‡K cÖavb A‡ÿi Ici IB j¤ Uvb‡j- IB n‡e

AB jÿ¨e¯‘i cÖwZwe¤| 9.26 wPÎ †_‡K †`Lv hvq cÖwZwe¤wU Am`, †mvRv Ges AvKv‡i jÿ¨e¯‘ †_‡K †QvU|

9.4.3 e ‘i wewfbœ Ae¯’v‡bi Rb¨ AeZj `c©Y Øviv m„ó cÖwZwe‡¤i Ae¯’vb, AvKvi Ges cÖK…wZ

(Position, Size and Nature of the immage formed by concave mirror) †Mvjxq `c©Y Øviv MwVZ cÖwZwe‡¤ Ae¯’vb, AvK…wZ I cÖK…wZ me †ÿ‡Î mgvb bq| †ÿÎ we‡k‡l Gi wewfbœZv ‡`Lv

hvq| Avi Zv wbf©i K‡i `c©‡Yi mvg‡b e¯‘i Ae¯’v‡bi Dci| A_©vr `c©‡Yi mvg‡b wewfbœ Ae¯’v‡b jÿ¨e¯‘ ¯’vcb

Ki‡j MwVZ cÖwZwe‡¤i Ae¯’vb, AvKvi I AvK…wZ wewfbœ nq| iwk¥ wPÎ Gu‡K Avgiv mn‡R NUbvwU ch©‡eÿY Ki‡Z

cvwi| wb‡P Q‡K AeZj `c©‡Yi †ÿ‡Î `c©YwUi mvg‡b cÖavb A‡ÿi Ici wewfbœ Ae¯’v‡b GKwU we¯Í…Z jÿ¨e¯‘i

Rb¨ MwVZ we‡¤i iwk¥ wPÎ we‡¤i Ae¯’vb, cÖK…wZ I AvK…wZ eY©bv Kiv n‡jv|

aiv hvK MM' GKwU AeZj `c©Y| P Gi †giæ, C eµZvi †K› ª, F cÖavb †dvKvm Ges PC cÖavb Aÿ| `c©YwUi

mvg‡b cÖavb A‡ÿi Ici wewfbœ Ae¯’v‡b GKwU we¯Í……Z jÿ¨e¯‘ OA| Ges jÿ¨e¯‘wUi wewfbœ †ÿ‡Î A'B' cÖwZwe¤

MVb K‡i‡Q|

µ. bs e¯‘i Ae¯’vb iwk¥ wPÎ cÖwZwe‡¤i Ae¯’vb cÖK…wZ I AvK…wZ

1 Amxg `~‡i

Ae¯’vbt †dvKvm Z‡j

cÖK…wZ t m` I D‡ëv

AvK…wZt AZ¨šÍ Lwe©Z

2 Amxg I

eµZvi

†K‡›`ªi g‡a¨

Ae¯’vbt eµZvi †K› ª I cÖavb

†dvKv‡mi g‡a¨

cÖK…wZ t m` I D‡ëv

AvK…wZt Lwe©Z

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 206

3 eµZvi †K‡› ª

Ae¯’vbt eµZvi †K‡› ª

cÖK…wZ t m` I D‡ëv

AvK…wZt jÿ¨e¯‘i mgvb

4 eµZvi †K› ª

I cÖavb

†dvKv‡mi

g‡a¨

Ae¯’vbt eµZvi †K› ª

I Amx‡gi g‡a¨

cÖK…wZ t m` I D‡ëv

AvK…wZt weewa©Z

5 cÖavb

†dvKv‡m

Ae¯’vbt Amx‡g

cÖK…wZ t m` I D‡ëv A_ev Am` I

†mvRv

AvK…wZt AZ¨šÍ weewa©Z

6 cÖavb †dvKvm

I †giæ we›`yi

g‡a¨

Ae¯’vbt `c©‡Yi †cQ‡b

cÖK…wZ t Am` I ‡mvRv

AvK…wZt weewa©Z

9.4.4 †MvjKxq `c©‡Y m„ó cÖwZwe‡¤i ˆewkó¨

9.4.3 Aby‡”Q‡`i wPÎmg~n †_‡K †`Lv hvq †h, AeZj `c©‡Yi †ÿ‡Î hLb jÿ¨e¯‘ Amxg `~j‡Z¡ _v‡K ZLb

cÖwZwe¤ `c©‡Yi cÖavb †dvKv‡m MwVZ nq Ges AvKvi AZ¨šÍ Lwe©Z nq| jÿ¨e¯‘‡K µgk mwi‡q Amxg `~iZ¡ †_‡K

eµZvi †K‡›`ª wb‡q G‡j cÖwZwe¤I µgk cÖavb †dvKvm †_‡K eµZvi †K‡›`ª m‡i Av‡m| GLv‡b me©‡ÿ‡Î cÖwZwe¤^

ev¯Íe I D‡ëv nq Ges Gi AvKvi jÿ¨e¯‘i †P‡q A‡bK †QvU †_‡K µgk eo n‡q eµZvi †K‡›`ª G‡m jÿ¨e¯‘i

mgvb nq|

jÿ¨e¯‘‡K eµZvi †K› ª †_‡K cÖavb †dvKv‡mi w`‡K mwi‡q Avb‡j cÖwZwe¤ eµZvi †K›`ª †_‡K Amx‡gi w`‡K

m‡i hvq| GLv‡bI me©‡ÿ‡Î cÖwZwe¤^ ev¯Íe, D‡ëv I AvKv‡i jÿ¨e¯‘i †P‡q µgk eo n‡Z _v‡K| jÿ¨e¯‘ cÖavb

†dvKv‡m _vK‡j cÖwZwe¤^ Amxg `~i‡Z¡ m‡i hvq Ges AvKvi AZ¨šÍ weewa©Z nq|

jÿ¨e¯‘‡K cÖavb †dvKvm †_‡K `c©‡Yi †giæi w`‡K mwi‡q wb‡j cÖwZwe¤ `c©‡Yi m¤§y‡L Amxg `~iZ¡ †_‡K `c©‡Yi

wcQ‡b P‡j hvq Ges µgk `c©‡Yi †giæi w`‡K m‡i Av‡m| G‡ÿ‡Î cÖwZwe¤ me© v Aev¯Íe, †mvRv Ges AvKv‡i

µgk †QvU n‡Z _v‡K| jÿ¨e¯‘ †giæ‡Z †cuŠQv‡j cÖwZwe¤ †giæ‡Z MwVZ nq| G‡ÿ‡Î cÖwZwe¤ Aev¯Íe, †mvRv Ges

AvKv‡i jÿ¨e¯‘i mgvb nq|

DËj `c©‡Y m„ó cÖwZwe¤ me© v Aev¯Íe I AvKv‡i jÿ¨e¯‘i †P‡q †QvU nq|

mvi-ms‡ÿc:

†MvjKxq `c©‡Yi MwVZ we‡¤i iwk¥ wPÎ A¼‡bi Rb¨ wZbwU iwk¥ we‡ePbv Kiv nq|

1. eµZvi e¨vmva© eivei AvcwZZ iwk¥, hv j¤fv‡e `c©‡Yi Dci c‡o, Ges cÖwZdj‡bi ci Avevi †mB c‡_B

wd‡i hvq|

2. cÖavb A‡ÿi mgvšÍivj AvcwZZ Av‡jvK iwk¥ hv cÖwZdj‡bi ci cÖavb †dvKvm eivei hvq|

3. cÖavb †dvKv‡mi eivei ev ga¨ w`‡q AvcwZZ Av‡jvK iwk¥ hv cÖwZdj‡bi ci cÖavb A‡ÿi mgšÍivj nq|

c`v_©weÁvb

BDwbU 9 c„ôv # 207

cv‡VvËi g~j¨vqb -9.4

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| wb‡Pi †KvbwU‡Z m` cÖwZwe¤ MwVZ nq?

(K) mgZj `c©‡Y (L) DËj `c©‡Y

(M) AeZj `c©‡Y (N) AeZj †j‡Ý

2| GKwU AeZj `c©‡Yi cÖavb A‡ÿi Dci Ges Zvi eµZvi †K‡› ª GKwU 0.5 cm j¤v

Avjwcb Lvovfv‡e ’vcb Ki‡j GKwU ev¯Íe we¤ Drcbœ nq| we¤wUi ˆ`N© KZ n‡e?

(K) 0.5 cm (L) 0.5 cm Gi A‡a©K

(M) 0.5 cm Gi wظY (N) ejv m¤¢e bq

3| GKwU jÿ¨e¯‘ AeZj `c©‡Yi cÖavb A‡ÿi Dci cÖavb †dvKvm I †giæ we›`yi g‡a¨ Aew¯’Z| we‡¤i Ae¯’vb

†Kv_vq n‡e?

(K) `c©‡Yi †cQ‡b (L) eµZvi †K› ª I Amx‡gi g‡a¨

(M) eµZvi †K‡› ª (N) eµZvi †K› ª I cÖavb †dvKv‡mi g‡a¨

4| †Mvjxq `c©‡Yi cÖwZdjK c„‡ôi ga¨we›`y‡K Kx e‡j?

(K) †K› ª (L) †giæ

(M) Aÿ (N) e¨vmva©

cvV- 5 weea©b (Magnification)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. AeZj `c©‡Yi †ÿ‡Î jÿ¨ e¯‘i `~iZ¡, cÖwZwe¤ `~iZ¡ Ges †dvKvm `~i‡Z¡i g‡a¨ m¤ú‡K©i mgxKiYwU

wjL‡Z cvi‡eb|

2. DËj `c©‡Yi †ÿ‡Î jÿ¨ e¯‘i `yiZ¡, cÖwZwe¤ ~iZ¡ Ges †dvKvm `~i‡Z¡i g‡a¨ m¤ú‡Ki© mgxKiYwU wjL‡Z

cvi‡eb|

3. weea©b e¨vL¨v Ki‡Z cvi‡eb|

4. weea©‡bi ivwkgvjv wjL‡Z cvi‡eb|

9.5.1 †MvjKxq `c©‡Y jÿ¨e¯‘i `~iZ¡, cÖwZwe‡¤i `~iZ¡ I †dvKvm ~i‡Z¡i m¤úK©

(Relation among Object distance, Image distance and Focal length of Spherical Mirror) Gi Av‡M 9.3.3 cv‡V Avgiv wk‡LwQ DËj `c©Y Ges AeZj `c©Y Dfq †ÿ‡ÎB `c©‡Yi †dvKvm `~iZ¡

Zvi eµZvi e¨vmv‡a©i A‡a©K| A_©vr †dvKvm `~iZ¡, f Ges eµZvi e¨vmva©, r n‡j

2rf Gcv‡V Avgiv Dfq cÖKvi †MvjKxq `c©‡Yi †ÿ‡Î jÿ¨e¯‘i `~iZ¡, cÖwZwe‡¤i `~iZ¡ Ges †dvKvm `~i‡Z¡

g‡a¨ m¤úK© wkL‡ev|

K. AeZj `c©‡Yi †ÿ‡Î

9.27 wP‡Î MPM GKwU AeZj `c©‡Yi cÖavb †Q`| P Gi †giæ we›`y Ges C eµZvi †K› ª | Gi cÖavb Aÿ PC

Gi Dci O we›`y‡Z GKwU we›`y jÿ¨e¯‘ ivLv n‡q‡Q| O we›`y †_‡K wbM©Z `ywU iwk¥i K_v Kíbv Kiv hvK| GKwU

iwk¥ cÖavb Aÿ eivei OP c‡_ A_v©r j¤fv‡e `c©Y Z‡j P we› y‡Z cwZZ nj| iwk¥wU wecixZ w`‡K PO c‡_

cÖwZdwjZ n‡e| Ab¨ GKwU iwk¥ Zxh©Kfv‡e `c©Y Z‡j Q we›`y‡Z cwZZ nj| cÖwZdj‡bi wbqg Abymv‡i GwUv

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 208

QIR c‡_ cÖwZdwjZ n‡e| d‡j cÖwZdwjZ iwk¥ `yÕwU PO Ges QR ci¯úi‡K I we›`y‡Z †Q` Ki‡e| myZivs I we›`y n‡e O we› y‡Z ’vwcZ we›`y e ‘i cÖwZwe‡¤i Ae¯’vb|

wPÎ t 9.27 AeZj `c©‡Y we›`y jÿ¨e ‘i we¤ MVb

GLv‡b 9.27 jÿ¨e¯‘i ~iZ¡, PO = u, cÖwZwe‡¤i `~iZ¡, PI = v Ges eµZvi e¨vmva©, PC = r n‡j,

+ =

ev, + = [

r = 2f ] ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ( 9.1 )

K. DËj `c©‡Yi †ÿ‡Î

aiv hvK (wPÎ 9.28) MPM GKwU DËj `c©‡Yi cÖavb †Q`| P Gi †giæ we›`y Ges C eµZvi †K›`ª | Gi cÖavb

Aÿ PC Gi Dci O we›`y‡Z GKwU we›`y jÿ¨e¯‘ ivLv n‡q‡Q| O we›`y †_‡K wbM©Z `ywU iwk¥i K_v Kíbv Kiv

hvK| GKwU iwk¥ cÖavb Aÿ eivei OP c‡_ A_v©r j¤fv‡e `c©Y Z‡j P we› y‡Z cwZZ nj| iwk¥wU wecixZ w`‡K

PO c‡_ cÖwZdwjZ n‡e| Ab¨ GKwU iwk¥ Zxh©Kfv‡e `c©Y Z‡j Q we›`y‡Z cwZZ n‡jv| cÖwZdj‡bi wbqg

Abymv‡i GwU QR c‡_ cÖwZdwjZ n‡jv| cÖwZdwjZ iwk¥ `ywU ci¯úi †_‡K `~‡i Qwo‡q hv‡”Q| G‡`i †cQ‡b

ewa©Z Ki‡j cÖavb A‡ÿi Dci ci¯úi‡K I we›`y‡Z †Q` Ki‡e| myZivs I we›`y n‡e O we›`y‡Z ¯’vwcZ we›`y e¯‘i

Am` cÖwZwe‡¤i Ae¯’vb|

wPÎ t 9.28 DËj `c©‡Y we› y jÿ¨e¯‘i cÖwZwe¤ MVb

GLv‡b 9.28 wP‡Î jÿ¨e¯‘i ~iZ¡, PO = u , cÖwZwe‡¤i ~iZ¡, PI = v Ges eµZvi e¨vmva©, PC = r n‡j,

+ =

ev, + = [

r = 2f ] ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ( 9.2)

c`v_©weÁvb

BDwbU 9 c„ôv # 209

9.5.2 ˆiwLK weea©b (Linear Magnification) mgZj `c©‡Y we‡¤i AvKvi Ges AvK…wZ jÿ¨e¯‘i AvKvi I AvK…wZi mgvb nq| wKš‘ †Mvjxq `c©Y Ges

†j‡Ýi †ÿ‡Î MwVZ cÖwZwe‡¤^i AvKvi jÿ¨e¯‘i mgvb, †QvU ev eo nq| cÖwZwe¤ jÿ¨e¯‘i Zzjbvq

KZ¸Y eo ev †QvU †mB ivwk‡K Zvi weea©b e‡j| Avgiv †Kv‡bv wemÍ„Z e¯‘i weea©b cwigv‡ci Rb¨ we‡¤i ˆ`N©

Ges jÿ¨e¯‘i ˆ`‡N© i AbycvZ‡K e¨envi Kwi| ZvB, we‡¤^i ˆ`N© Ges jÿ¨e¯‘i ˆ`‡N© i AbycvZ‡K ˆiwLK weea©b

e‡j|

aiv hvK †Kv‡bv jÿ¨e ‘i ˆ`N© Lo Ges cÖwZwe‡¤i ˆ`N© Li| Zvn‡j,

ˆiwLK weea©b

i

o

Lm

L

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

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

9.5.3 ˆiwLK weea©‡bi ivwkgvjv

`c©Y AeZj ev DËj hvB †nvK, cÖwZwe¤ ev Íe ev Aev¯Íe Ges †mvRv ev D‡ëv hvB †nvK weea©b n‡e,

m = - vu ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (9.3)

GLv‡b u = `c©‡Yi †giæ †_‡K jÿ¨e¯‘i ~iZ¡ Ges v = `c©‡bi †giæ †_‡K cÖwZwe‡¤i `~iZ¡| weea©‡bi cig gvb

|m| = - vu ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (9.4)

MvwYwZK D`vniY 9.1

15cm †dvKvm `~i‡Z¡i †Kv‡bv AeZj `c©Y †_‡K 10 cm `~‡i GKwU e¯‘ ¯’vcb Kiv njv | cÖwZwe‡¤i Ae¯’vb I

cÖK…wZ wbY©q Kiæb|

mgvavb t

Avgiv Rvwb,

1 1 1

v u f

ev,

1 1 1 1 1 115cm 10cm 30cm

v f u

ev, v = -30cm

DËi t cÖwZwe‡¤i `~iZ¡ †h‡nZz we‡qvM †evaK myZivs we¤wU

Am`|

GLv‡b,

`c©‡Yi †dvKvm ~iZ¡, f = 15 cm,

e¯‘i ~iZ¡, u = 10 cm

we¤ ~iZ¡ v = ?

MvwYwZK D`vniY 9.2

GKwU AeZj `c©‡Yi 20 cm mvg‡b GKwU †gvgevwZ ivL‡j 35 cm mvg‡b c`©vi Dci †gvgevwZwUi GKwU D¾¡j

D‡ëv cÖwZwe¤ m„wó nq| cÖwZwe¤wUi ˆiwLK weea©‡bi cwigvY wbY©q Kiæb|

mgvavbt

Avgiv Rvwb, ˆiwLK weea©Y,

m vu

GLv‡b, e¯‘ ~iZ¡, u =20 cm

cÖwZwe¤ `~iZ¡, v = 35 cm

ˆiwLK weea©b, m = ?

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 210

ev,

|m| = vu

ev, |m| = 3520

= 1.75

DËi t 1.75

mvi-ms‡ÿc:

GKwU †MvjKxq A_©vr AeZj ev DËj `c©‡bi mvg‡b ¯’vwcZ jÿ¨e¯‘ †_‡K Drcbœ cÖwZwe‡¤i †ÿ‡Î

jÿ¨e¯‘i `~iZ¡ = u, cÖwZwe‡¤i `~iZ¡ = v Ges `c©‡Yi ‡dvKvm `~iZ¡ = f n‡j

+ =

†MvjKxq `c©‡Yi †ÿ‡Î †giæ we›`y mv‡c‡ÿ ~iZ¡‡K abvZ¥K ev FYvZ¥K wVK Kiv nq| Av‡jvi ~iZ¡ Av‡jvi w`‡K

n‡j abvZ¥ Ges Av‡jvi wecixZ w`‡K n‡j FYvZ¥K aiv nq|

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

o

LL

Ges

jÿ¨e¯‘i ~iZ¡, u Ges cÖwZwe‡¤i `~iZ ¡ v n‡j, ˆiwLK weea©b

vmu

m Gi gvb abvZ¥K n‡j we¤ †mvRv n‡e| FYvZ¥K n‡j we¤wU D‡ëv n‡e|

m > 1 n‡j, cÖwZwe¤wU weewa©Z n‡e| m = 1 n‡j, cÖwZwe¤wU jÿ¨e ‘i mgvb n‡e|

m < 1 n‡j, cÖwZwe¤wU †QvU ev Lwe©©Z n‡e|

cv‡VvËi g~j¨vqb -9.5

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| DËj `c©‡Yi †ÿ‡Î †KvbwU mwVK ?

(K) eµZvi e¨vmva© = †dvKvm ~iZ¡ (L) †dvKvm ~iZ¡ = 2 eµZvi e¨vmva©

(M) eµZvi e¨vmva© = 2 †dvKvm ~iZ¡ (N) eµZvi e¨vmva© =

21†dvKvm ~iZ¡

2| + = mgxKiYwU‡Z u Øviv wK eySvb nq?

(K) †giæ we› y †_‡K jÿ¨e ‘i `~iZ¡ (L) †dvKvm we›`y †_‡K cÖwZwe¤ ~iZ¡

(M) †giæ we›`y †_‡K cÖwZwe‡¤i ~iZ¡ (N) †dvKvm we›`y †_‡K jÿ¨ e ‘i `~iZ¡

3| †Kvb †Kvb Z_¨ †`qv _vK‡j Avcwb GKwU AeZj `c©‡Yi †dvKvm ~iZ¡ ej‡Z cvi‡eb?

(K) eµZvi e¨vmva© (L) we¤ ~iZ¡

(M) e¯‘ ~iZ¡ (N) `c©Y Z‡ji †ÿÎdj

c`v_©weÁvb

BDwbU 9 c„ôv # 211

cvV -6 `c©‡Yi e¨envi (Uses of Mirror)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb -

1. mgZj `c©Y I †Mvjxq `c©‡Yi e¨envwiK cÖ‡qvM eY©bvmn D‡jøL Ki‡Z cvi‡eb|

9.6.1 mgZj `c©‡Yi e¨envi (Uses of Plane Mirror)

mgZj `c©Y Avgv‡`i ‰`bw›`b Rxe‡b AwZ eûj e¨eüZ GKwU DcKiY|GB `c©Y‡K Avgiv Avqbv ewj| Avqbv

e¨envi K‡ib bv Ggb gvbyl we‡k¦ weij| wb‡P Avqbvi wKQz e¨envi D‡jøL Kiv n‡q‡Q|

1| mgZj `c©Y wb‡Ri †Pnviv †`Lvi Rb¨, wb‡Ri †cvlvK cwi”Q`, mvR m¾vi Ae¯’v wb‡R hvPvB Kivi Rb¨,

we‡kl K‡i †Wªwms †Uwe‡j mgZj `c©‡Yi e¨envi ˆ`bw›`b Rxe‡bi NUbv|

2| †Pv‡Li Wv³vi †ivMxi `„wó cixÿvi Rb¨ GKwU Aÿ‡ii PvU© (†¯œj PvU©) e¨envi K‡ib, GwUi `~iZ¡ wbw`©ó Kivi

Rb¨ mgZj `c©Y e¨envi K‡ib|

3| †cwi‡¯‹vc ˆZwi‡Z mgZj `c©Y e¨eüZ nq|

4| cvnvox iv¯Ívq evuK _vK‡j Mvoxi PvjK evuK ch©šÍ bv G‡j Zv †`L‡Z ev eyS‡Z cv‡ib bv d‡j gvivZ¥K `yN©Ubv

N‡U| Gai‡bi iv¯Ívi euv‡K wekvj AvKvi GKwU mgZj `c©Y 45 wWwMÖ †KvY K‡i ewm‡q ivLv nq G‡Z `c©‡Yi

g‡a¨ D‡ëv w`K †_‡K Avmv hvbevnb `„wó †MvPi nq| d‡j `yN©Ubv Gov‡bv hvq|

5| wewfbœ ai‡bi Av‡jvK hš¿ †hgb- Ifvi †nW cÖ‡R±i, †Uwj‡¯‹vc, K¨v‡giv, M¨vjfv‡bvwgUvi, †jRvi BZ¨vw`

ˆZwi‡Z mgZj `c©Y e¨envi Kiv nq|

6| PjwPÎ ev wm‡bgv mywUs Gi mgq Av‡jvi gvÎv evovbi Rb¨ wekvj wekvj AvKv‡ii mgZj `c©Y e¨eüZ nq|

7| †`vKvb cvU ev wekvj wekvj kwcs g‡j we‡kl K‡i Ry‡qjvwi †`vKv‡b †mŠ›`h© e„w× I AvKl©Yxq Kivi Rb¨

mgZj `c©Y e¨envi Kiv nq|

8| †mjyb, weDwU cvj©vi, bvUK w_‡qUvi cÖf…wZi †gKAvc iæ‡g Dfq w`‡K †`qvj Ry‡o mgZj `c©‡Yi e¨envi ‡`Lv

hvq|

9.6.2 †MvjKxq `c©‡Yi e¨envi (Use of Spherical Mirror) wewfbœ e¨envwiK Kv‡R Avgiv AZj `c©Y I DËj `c©Y e¨envi Kwi| †Kv‡bv †Kv‡bv †ÿ‡Î Gme e¨envwiK cÖ‡qvM

AvaywbK Rxeb hvÎvi Rb¨ Acwinvh©| Gai‡bi K‡qKwU e¨envi D‡jøL Kiv n‡jv|

AeZj `c©Y t

AeZj `c©‡Yi cÖwZdjK Zj wbPz| GwU Av‡jvK iwk¥‡K ev¯Í‡e GKwU we›`y‡Z †K› ªxf~Z Ki‡Z cv‡i, d‡j GwU m`

I Am` Dfq cÖKv‡ii we¤ MVb Ki‡Z cv‡i| GRb¨ Gi e¨envi e¨vcK| wb‡P K‡qKwU ¸iæZ¡c~Y© e¨envi mvgvb¨

e¨vL¨vmn D‡jøL Kiv n‡q‡Q|

1. m¨v‡UjvBU wWm Gw›Ubvq AeZj `c©Y e¨envi Kiv nq| KwgDwb‡Kkb

m¨v‡UjB‡Ui gva¨‡g †cÖiK Gw›Ubvmg~n ZvwoZ‡PŠ¤Kxq Zi½‡K

gnvk~‡b¨ Qwo‡q †`q| †h‡nZz c„w_ex †_‡K m¨v‡UjvBU¸‡jvi ~iZ¡

A‡bK †ewk ZvB c„w_ex‡Z Avmv `ye©j Zi½¸‡jv cÖvq mgvšÍivjfv‡e

AeZj Z‡j AvcwZZ nq Ges cÖwZdj‡bi wbq‡g †dvKv‡m wgwjZ nq|

AvMZ `ye©j Zi½ GKwU ‡dvKv‡m wgwjZ nIqvq †ek †Rvivj nq|

AZci GwU ewa©Z K‡i MÖvnK h‡š¿ †cÖwiZ nq|

wPÎ t 9.29 m¨v‡UjvBU wWm

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 212

2. gyLgÛ‡ji weewa©Z cÖwZwe¤ †`Lvi Rb¨ GK ai‡Yi we‡kl weea©K

Avqbv e¨eüZ nq| hvi g‡a¨ ZvKv‡j `k©K wb‡Ri †Pnviv ev gy_

gÛjwU †ek K‡qK ¸Y eo †`L‡Z cvb| GwU AeZj `c©Y|cyiæl‡`i

`uvwoKvUvi †ÿ‡Î Ges †g‡q‡`i gyLgÛ‡ji cwiPh©vmn åæ cøvwKs Kv‡R

eûj e¨eüZ nq|

3. GKwU AeZj `c©‡Yi †dvKvm we›`y‡Z GKwU AwaK kw³i ˆe`y¨wZK

evj¦¦ ewm‡q Mvwoi †nW jvBU ˆZwi Kiv nq| evj¦‡ei Av‡jv `c©Y Zj

Øviv cÖwZdwjZ n‡q mgvšÍivj iwk¥ iƒ‡c mvg‡b Qwo‡q c‡o|

4. gnvk~Y¨ M‡elYvi Rb¨ GKwU AZ¨šÍ Riæix DcKiY n‡jv †Uwj‡¯‹vc ev

`~iexY hš¿| B`vwbs me ai‡Yi †Uwj‡¯‹v‡c cÖwZdjK AeZj `c©Y

e¨eüZ nq| AeZj `c©YwU †Uwj‡¯‹v‡ci Zjvq emv‡bv nq `c©©‡Yi

Dci `~i †R¨vwZ®‹ †_‡K Avmv ÿxY Av‡jvi AvcwZZ iwk¥mg~n GKwU

†dvKv‡m wgwjZ n‡q D¾¡j nq Ges †dvKv‡m ¯’vwcZ GKwU mgZj

`c©‡Y cÖwZdwjZ n‡q AvB wc‡mi gva¨‡g †Pv‡L ev K¨v‡givq c‡o|

wPÎ t 9.30 weea©K Avqbv

wPÎ t 9.31 wi‡d¬±i †Uwj‡¯‹vc

5. Mvwoi †nW jvB‡Ui g‡Zv UP© jvB‡Ui wi‡d¬±i Ges K¨v‡givi d¬vm jvB‡Ui wi‡d¬±i wnmv‡e AeZj `c©Y

e¨eüZ nq|

6. `uv‡Zi Wv³viiv cÖK…Z `uvZ †_‡K eo cÖwZwe¤

†`L‡Z Ges we‡kl K‡i Dci cvwUi `uvZ

†`L‡Z nvZj hy³ wi‡d¬w±s wgii e¨envi

K‡ib| G‡ÿ‡Î AeZj `c©Y e¨eüZ nq|

7. wekvjvKvi avZe AeZj `c©Y w`‡q †mŠi Pzwjø

wbg©vY Kiv nq| Gi Dci cwZZ mgvšÍÍivj m~h©

iwk¥ †dvKvm we›`y‡Z †K›`ªxf~Z n‡q ch©vß Zvc

Drcbœœœ K‡i| H we›`y‡Z ivbœvi cvÎ ewm‡q

Abvqv‡m cvwb Mig ev ivbœvi KvR Kiv hvq|

wPÎ 9.34 wi‡d¬w±s †gii

wPÎ 9.32†mŠiPzwjø

8. me ai‡Yi gvB‡µvm‡Kvc ev AYyexÿY h‡š¿ Ggb wK B‡j±ªb gvB‡µv‡¯‹vc h‡š¿I weea©K Kv‡Pi mv‡_ AeZj

`c©Y e¨eüZ nq|

DËj `c©Y t

DËj `c©‡Yi cÖwZdjK Zj DPz _v‡K| GwU AvcwZZ Av‡jvK iwk¥‡K Pvwiw`‡K Qwo‡q †`q| GB `c©‡Y memgq

Am`, †mvRv Ges jÿ¨e¯‘ †_‡K †QvU cÖwZwe¤ MwVZ nq, ZvB †h me †ÿ‡Î eo AvKv‡ii ev †ewk GjvKvi `„k¨

mn‡R GK mv‡_ †QvU K‡i †`Lvi cÖ‡qvRb †m me †ÿ‡Î DËj `c©Y e¨envi Kiv nq| Avvgiv 8wU ¸iæZ¡c~Y© e¨envi

mvgvb¨ e¨vL¨vmn D‡jøL KiwQ|

1. eo eo feb nvmcvZvj, Awdm ev kwcs g‡j gv‡S gv‡S DËj `c©Y emvb nq G‡Z cy‡iv Zjvi g‡a¨ †Kv_vq Kx

Av‡Q GK RvqMvq `uvwo‡q LywUbvwU †`Lv hvq Ges †jvKRb PjvP‡j ci¯ú‡ii mv‡_ av°v avw°i SuzwKI Gov‡bv

hvq|

2. GK ai‡Yi wekvjvKvi DËj `c©Y gw›`i, gmwR`, mwcs Kg‡cø·Ñ wewfbœ RbmgvMg ¯’v‡b Dci †_‡K Szwj‡q

†`qv nq| GZ wb‡Pi mg¯Í GjvKv GK m‡½ ch©‡eÿY Kiv hvq| G‡`i ejv nq mxwjs †Wvg wgii| GwU fe‡bi

Qv‡`i mv‡_ †KvYvq, cv‡k ev †K› ª eiveiI ¯’vcb Kiv nq|

c`v_©weÁvb

BDwbU 9 c„ôv # 213

wPÎ t 9.33 wewfbœ ai‡bi wmwjs †Wvg wgii

2. mvbMøv‡m DËj `c©Y e¨envi Kiv nq| G‡Z mvbMøvm cwiwnZ e¨vw³i †Pv‡L cwZZ †mŠi iwk¥ cÖwZdwjZ n‡q

†PvL‡K DËvc I Zxÿ Av‡jv †_‡K iÿv K‡i|

3. †gvUi Mvox, †gvUi mvB‡Kj BZ¨vw` `ªæZMvgx Mvwoi Pvj‡Ki

mvg‡b GKwU DËj `c©Y _v‡K| G‡K ejv nq wiqvi wfD

wgii| PvjK Mvwo Pvjv‡bvi mgq †cQ‡bi `„k¨ †`Lvi Rb¨

GwU cÖ‡qvRb nq|

G‡Z †cQb †_‡K Avmv Mvwo Ges †cQ‡bi w`‡Ki we¯ÍxY©

GjvKvi wPÎ GK mv‡_ Pvj‡Ki †Pv‡L c‡o| wiqvi wfD wgii

PvjK‡K A‡bK iKg `~N©Ubv †_‡K iÿv Ki‡Z cv‡i|

wPÎ t 9.34 †iqvi wfD wgii

4. B`vwbs kn‡ii iv¯Ívq A‡bK GwUGg ey_ †Pv‡L c‡i| GB ey‡_

MÖvn‡Ki mvg‡b †`qv‡j DËj `c©Y jvMv‡bv _v‡K| G‡Z ey_

e¨enviKvix Zvi †cQ‡b †KD Av‡Q wKbv wbixÿY Ki‡Z cv‡ib|

GwU GKwU wbivcËvg~jK e¨e¯’v| G‡Z WvKvZ wQbZvBKvixi †_‡K

mZK© _vKv hvq|

5. †h me GjvKvq ev hvqMvq mn‡R hvIqv hvqbv ev †XvKv m¤¢e nq bv

†mme ¯’vb †`Lv ev wbixÿ‡Yi Rb¨ GKwU mwVK gv‡ci jvwVi mv‡_

GKwU DËj `c©Y Ges Av‡jvi Drm jvwM‡q †bqv nq| Mvoxi Zjv

cixÿv Kiv Rb¨ cywjk †PK †cvó ev ¸iæZ¡c~Y© fe‡b Gi e¨vcK

e¨envi †`Lv hvq| Mvwo †givg‡Zi KvRmn wewfbœ KvwiMwi Kv‡R

Gi e¨envi †Pv‡L c‡o|

wPÎ t 9.35 Mvoxi Zjv wbixÿY `c©Y

6. ivmÍvi Av‡jv cÖwZdjK wnmv‡e †Kvb †Kvb †`‡k iv¯Ívq wekvj wekvj mvB‡Ri avZe DËj `c©Y emvb nq| GB

`c©Y we¯ÍxY© GjvKvq Av‡jv Qwo‡q w`‡Z cv‡i|

7. A‡bK hvqMvq iv¯Ívi euv‡K wekvj mvB‡Ri avZe DËj `c©Y emvb nq| G‡Z ev‡Ki Kvi‡Y `~i †_‡K †_‡K

AvMZ †hme Mvwo, hv eivei ZvwK‡q `„wó †MvPi nIqv m¤¢e bq Zv †`Lv hvq| d‡j gvivZ¥K msNl© Gov‡bv

hvq|

mvi-ms‡ÿc:

mgZj `c©‡Yi e¨envi : wb‡Ri †Pnviv †`Lv, †Wªwms †Uwej, `„wó cixÿv PvU© †`L‡Z, †cwi‡¯‹vc, †Uwj‡¯‹vc

†nWcÖ‡R±i, K¨v‡giv, M¨vjfv‡bvwgUv‡i, wm‡bgv mywUs, †`vKvb cv‡U, †mjyZb weDwU cvj©vi iv¯Ívi euvK †`L‡Z|

‡MvjKxq `c©‡Yi e¨envi : wewfbœ e¨envwiK Kv‡R Avgiv AeZj `c©Y I DËj `c©Y e¨envi Kwi| †Kvb †Kvb

†ÿ‡Î Gme e¨envwiK cÖ‡qvM AvaywbK Rxeb hvÎvi Rb¨ Acwinvh©|

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 214

cv‡VvËi g~j¨vqb -9.6

mwVK Dˇii cv‡k wUK ( ) wPý w`b|

1| DËj `c©Y e¨envi nq †Kv_vq?

(K) GwU Gg ey‡_ (L) ‡mŠi Pzwjø wbg©v‡Y

(M) iƒcPP©vq (N) UP© jvB‡Ui wi‡d¬±‡i

2| GKwU 25 cm †mwg †dvKvm ˆ`‡N©i AeZj `c©‡Yi mvg‡b 50 cm `~‡i GKwU jÿ¨ e¯‘ ivL‡j `c©b †giæ †_‡K

KZ ~‡i cÖwZwe¤ ˆZwi n‡e?

(K) 25 cm (L) 50 cm (M) 100 cm (N) 12.5 cm

cvV 7t e¨envwiK -11 AeZj `c©Y e¨envi K‡i cªwZwe¤ m„wó

Creation of Image using Concave Mirror

D‡Ïk¨

GB cvV †k‡l Avcwb

1. AeZj `c©Y e¨envi K‡i ev Íe cÖwZwe¤ m„wó I cÖ k©b Ki‡Z cvi‡eb|

hš¿cvwZ t GKwU AeZj `c©Y

Kvh© cÖYvjx t

1| GKwU AeZj `c©Y msMÖn Kiæb| (evmvq m¤¢e bvI n‡Z cv‡i| j¨ve‡iUwi‡Z cv‡eb|)

2| `c©YwU wb‡q Avcwb GKwU Rvbvjvi cv‡k ev eviv›`vq hvb| (Ggb GKwU hvqMv †e‡Q wbb †hLv‡b N‡ii ev

eviv›`vi g‡a¨ Qvqv Av‡Q ev mivmwi m~‡h©i Av‡jv co‡Q bv|)

3| N‡ii evB‡i jÿ¨ Kiæb 1-2 wgUvi `~i‡Z¡i g‡a¨ †hLv‡b †Kvb e ‘i Dci mivmwi m~‡h©i Av‡jv co‡Q †hb

jÿ¨e¯‘wU D¾¡j †`Lv cvq|

4| `c©‡Yi cÖwZdjK wcVwU jÿ¨e¯‘i w`‡K gyL K‡i Ggbfv‡e aiæb †hb jÿ¨e¯‘ †_‡K Av‡jv G‡m `c©Y c„‡ô

c‡o cÖwZdwjZ n‡q Rvbvjvi cv‡k cwi®‹vi †`qv‡ji (eviv›`vq n‡j, eviv›`vi †Kvb †`qv‡ji) c„‡ô c‡o|

`c©YwU mvgvb¨ mvg‡b †cQ‡b KvZ K‡i, Wv‡b ev‡g

Nywi‡q †Póv Ki‡Z Ki‡Z µgk †`qv‡ji w`‡K GwM‡q

†h‡Z _vKzb| GK mgq †`qv‡j jÿe¯‘i `„‡k¨i we¤^

co‡e| GwUB cÖwZwe¤|

wPÎ 9.36

5| cÖwZwe¤wU‡K ¯úó Kivi Rb¨ `c©YwU‡K †`qvj †_‡K mvg‡b †cQ‡b mivb| †Kvb GK Ae¯’v‡b jÿ¨e¯‘wUi

¯úó cÖwZwe¤ †`qv‡j †`L‡Z cv‡eb (wPÎ 9.36)|

Gfv‡e †`qv‡j ~‡ii e¯‘i ®úó cÖwZwe¤ †`Lv hvq| GwU ev Íe ev m` we¤| we¤wU Ab¨‡K †`Lvb|

Gevi wb‡Pi cÖkœ ‡jvi DËi w`bt

(1) Avcbvi m„wó Kiv cÖwZwe¤wUi AvKvi AvK…wZ Ges ˆewkó Kx?

(2) `c©YwU w`‡q GKwU Am` cÖwZwe¤ MVb Ki‡Z cvi‡eb Kx?

(3) (`c©YwUi Lye Kv‡Q GKwU Kjg ev †cwÝj A_ev Avcbvi nv‡Zi GKwU Av½yj AvovAvwo K‡i aiæb|

c`©‡Yi g‡a¨i QvqvwU †`Lyb| Kx †`L‡Qb ? †Kb Ggb †`Lv‡”Q? GwU †Kvb ai‡bi we¤?

wb‡Pi e‡· ev LvZvq cÖwZwe¤wU MV‡bi iwk¥ wPÎ AuvKzb Ges Gi cÖK…wZ I ˆewk󨸇jv wjLyb|

c`v_©weÁvb

BDwbU 9 c„ôv # 215

P‚ovšÍ g~j¨vqb-9

K. mvaviY eûwbe©vPbx cÖkœ t

mwVK Dˇii cv‡k wUK () wPý w`b|

1| GKwU we‡¤i c~Y© weeiY wjL‡Z wb‡Pi †Kvb welqwU D‡jøL Ki‡Z nq?

(K) we‡¤i Ae¯’vb (L) we‡¤i cÖK…wZ

(M) we‡¤i AvK…wZ (N) me¸‡jvB

2| GKwU we›`y e ‘i cÖwZwe¤ MV‡bi iwk¥ wPÎ AuvK‡Z Kg c‡¶ KZwU iwk¥ we‡ePbv Ki‡Z n‡e?

(K) 1wU (L) 2wU

(M) 3 wU (N) 4wU

3| GKwU j¶¨e¯‘ AeZj `c©‡Yi cÖavb A‡¶i Dci cÖavb †dvKv‡m Aew¯’Z| we‡¤i Ae¯’vb †Kv_vq n‡e?

(K) `c©‡Yi †cQ‡b μ(L) e Zvi †K‡› ª

(M) Amx‡g μ(N) e Zvi †K›`ª I Amx‡gi g‡a¨

4| GKwU e¯‘i ˆ`N¨© 0.3m Ges †Mvjxq `c©‡Yi ˆiwLK weea©b 2 n‡j we‡¤i •`N© KZ n‡e?

(K) 0.06 m (L) 0.6 m

(M) 6 m (N) 60 m

5| AeZj `c©‡Y cÖavb A‡¶i Dci eμZvi †K‡›`ª Aew¯’Z j¶¨e¯‘i we‡¤ cÖK…wZ Kxiƒc n‡e?

(K) m` I D‡ëv (L) Am` I †mvRv

(M) m` I †mvRv (N) K A_ev L

L. eûc`x mgvwß m~PK cÖkœ t

1| AeZj `c©‡Yi ˆewkó¨ n‡jv-

i. `c©‡Yi mvg‡b jÿ¨ e¯‘i Lwe©Z m` we¤ m„wó Ki‡Z cv‡i|

ii. `c©‡Yi †cQ‡b jÿ¨ e ‘i ewa©Z Am` we¤ m„wó Ki‡Z cv‡i|

iii. `c©‡Yi mvg‡b jÿ¨ e¯‘i ewa©Z m` we¤ m„wó Ki‡Z cv‡i|

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

GmGmwm †cÖvMÖvg

BDwbU 9 c„ôv # 216

M. Awfbœ Z_¨ wfwËK cÖkœ t

Wvb w`‡Ki wPÎwU †`Lyb, MP GKwU `c©Y| P Gi †giæ we›`y, C

eµZvi †K› ª, F †dvKvm we› y Gi mvg‡b evgw`‡K wZbwU jÿ¨e¯‘

1, 2, I 3 ivLv n‡q‡Q d‡j 3, 2 I 1 wZbwU cÖwZwe¤ m„wó n‡q‡Q|

wPÎwU fvjfv‡e jÿ¨Kiæb| wb‡Pi 1-2 ch©šÍ cÖkœ ‡jvi DËi w`b|

1| wP‡Îi 2 b¤i jÿ¨e¯‘ †_‡K m„ó cÖwZwe¤wUi ˆewkó¨ wK?

(K) m` I D‡ëv (L) Am` I †mvRv

(M) m` I †mvRv (N) Am` I D‡ëv

2| GB `c©‡Yi mvg‡b †Kv_vq jÿ¨ e¯‘ ivL‡j ewa©Z cÖwZwe¤ m„wó n‡e?

(K) cÖavb †dvKv‡m (L) eµZvi †K‡› ª

(M) Amxg `~i‡Z¡ (N) GB `c©Y Øviv ewa©Z we¤ m¤¢e bq

N. m„Rbkxj cÖkœ t

wP‡Î GKwU AeZj `c©‡Yi cÖavb A‡ÿi Dci GKwU e¯‘ AB Lvov K‡i

emv‡bv| †`Lv hv‡”Q| `c©YwUi †giæ we›`y P, cÖavb †dvKvm F, eµZvi

†K›`ª C| `c©‡Yi mvg‡b AB e¯‘i A′B′ cÖwZwe¤ MwVZ n‡q‡Q| wP‡Î

cÖwZwe¤ MVb Ges iwk¥ wPÎ AuvKv bvB| wb‡Pi cÖkœ ‡jvi DËi w`b|

K. cÖwZwe¤ Kv‡K e‡j|

L. m` I Am` cÖwZwe‡¤i cv_©K¨ wK ?

M. wPÎwU m¤ú~Y© K‡i Gu‡K MwVZ cÖwZwe‡¤i Ae¯’vb I AvKvi D‡jøL Kiæb|

N. MwVZ cÖwZwe¤wU m` bv Am` ? m` n‡j GB `c©Y w`‡q wKfv‡e Am` cÖwZwe¤ cvIqv hv‡e? A_ev Am` n‡j

wKfv‡e m` cÖwZwe¤ cvIqv hv‡e wPÎ Gu‡K e¨vL¨v Kiæb|

eûwbe©vPbx cÖkœmg~‡ni DËigvjv

cv‡VvËi g~j¨vqb 9.1 t 1| (L) 2| (K) 3| (L)

cv‡VvËi g~j¨vqb 9.2 t 1| (N) 2| (N) 3| (N) 4| (K)

cv‡VvËi g~j¨vqb 9.3 t 1| (N) 2| (N)

cv‡VvËi g~j¨vqb 9.4t 1| (M) 2| (K) 3| (K) 4| (L)

cv‡VvËi g~j¨vqb 9.5t 1| (M) 2| (K) 3| (K)

cv‡VvËi g~j¨vqb 9.6 t 1| (K) 2| (L)

PzovšÍ g~j¨vqb -9

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

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

M. Awfbœ Z_¨ wfwËK eûwbe©vPbx cÖkœ t 1| (L) 2| (N)