hkkx - iwave optics reg. & corp. office: cg tower, a-46 & 52, ipia, near city mall, jhalawar...

Wave Optics

Reg. & Corp. Office: CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)- 324005

Website : www.resonance.ac.in | E-mail : [email protected] ADVWO - 1

Toll Free : 1800 258 5555 | CIN : U80302RJ2007PLC024029

Hkkx - I [k.M (A)

A-1. ges Kkr gS fd res = 1 + 2 + 2 1 2 cos ()

(a) res = + 4 + 2 × 2 cos (0) = 9 I.

(b) res = + 4 + 2 × 2 cos 2

= 5 I.

(c) res = + 4 + 2 × 2 cos (180) = I. A-2. Kkr gS fd fdlh izdk'k rjax ds fy,

E = E0 sin (t – kx )

rjax dh pky v = k

bldh nh xbZ lehdj.k ls rqyuk djus ij v = 3 × 104 × 5 × 10–7 v = 15 × 107 m/s

;gk¡ 14

x ox 7

yE (y,t) E sin2 3 10 t

5 10

= vk

vc =C

v =

7

7

30 10 m / s

15 10 m/ s

= 2.

[k.M (B)

B-1. Kkr gS fd = D

d

(a) ;fn D c<+sxk c<+sxk

vr% fÝat pkSM+kbZ c<+sxh

(b) ?kVsxk ?kVsxk

(c) d c<+sxk ?kVsxk

;fn L=kksr f>jhZ ¼fLyV½ dks fudV yk;k tk, rks , D o d vizHkkfor jgrs gSa] vr% leku gh jgrk gSA

(d) fLyVksa dh pkSM+kbZ FkksM+h c<+kus ij ge dsoy vkifrr iqat dh rhozrk dks c<+k jgs gSaA fQj ls , D, d esa dksbZ

ifjorZu ugha vr% vifjofrZr jgrh gSa ijUrq fÝatksa dh ped c<+ tkrh gSA B-2. pwafd D >>d & << d.

vr% iz;qDr dj ldrs gS = D

d

5th nhIr o 3rd vnhIr fÝUt ds chp nwjh = 5 – (2 + /2)

= 5

2 =

–7

3

5 6.5 10 1

2 10

= 1.625 mm

Wave Optics




B-3. AS D

d

= 0.4 mm

ifjofrZr djus ij cu tk,xk

’ =3

4 × 0.4 = 0.3 mm.

B-4. pwafd << d; iz;qDr dj ldrs gS

=D

d

so

D d

=

10

3

6000 10

3 10

= 2 × 10–4 jsfM;u

=180

× 2 × 10–4 degree fMxzh = 0.011º

[k.M (C) C-1. As pwafd << d

1 = 1 D

d

2 = 2 D

d

So vr%, 2 – 1 = 2 1– D

d

=

9

3

700 – 580 10 1.5

0.20 10

= 0.9 mm.

[k.M (D) D-1. (a) ifêdk j[kus ij, vifjofrZr jgrh gS

= D

d

=

9

2

480 10 1 m

0.12 10

= 4.0 × 10–4 m.

(b) 'kwU; iFkkUrj okys fcUnq Kkr djrs gS (dsUnzh; mfPp"B)

vr%] P ij vfrfjDr iFk (i.e. dsin) ds dkj.k iFkkUrj izdk'kh; iFkkUrj ds rqY; gksuk pkfg,A

dsUæh; fcUnq ij iFkkUrj = (2 – 1) t = 83.33

D;ksafd ge Åij dh vksj 2

3

xfr djrs gSa blfy, iFkkUrj ?kVrk gSA vr%

3

Å¡pkbZ ij ge mfPp"B izkIr djrs gSa

rFkk uhps dh vksj nwjh ij mfPp"B cusxkA D-2. Li"Vr% izdk'kh; iFkkUrj

= ( – 1) t = 4

t =

4( – 1)

.

Wave Optics




[k.M (E) E-1.

Li"Vr% O ij iFkkUrj ugh gksxk

iFkkUrj = S1 Q

= d cos (90–) = d sin.

= d × 2d

=

2

ifj.kkeh iFkkUrj

vr% = 2

2

± ( – 1)t.

2

= ± ( – 1) 2( 1)

2

= 2, 0

lEiks"kh O;frdj.k vr% Ires = vf/kdre

[k.M (F) F-1. iFkkUrj 2t gS

fouk'kh O;frdj.k ds fy, ;g gks ldrk gSA

2t =2

or

3

2

;k or 5

2

o blh izdkj .........

=4t

, 3

4t

,

5

4t

.....

=9

6

580 10

4 0.3 10

, 9

6

3 580 10

4 0.3 10

................

= 0.4833 , 3 × 0.4833.............. vr = 3 × 0.4833 = 1.45 mÙkj gS ,{1.3 < < 1.5} F-2. Li"V :i ls ean (nqcZy) ijkoZru ds fy, ;g fouk'kh O;frdj.k gksuk pkfg,

2t = 2

{U;wure eksVkbZ ds fy, }

t = 4

= 9560 10

4 1.4

= 100 nm

[k.M (G) G 1. izFke mfPp"V ds fy,

sinm =

1m

2

a

sin1 = 3

2a

or a = 1

3

2sin

= 73 6 10

2 sin30º

= 1.8 m

Wave Optics




(ii) izFke fufEu"V ds fy,

sinm = m

a

or sin 1 =a

a = 1sin

a = 76 10

sin30º

= 1.2 m

Hkkx - II

[k.M (A) A-1. KkrO; gS I A2.

2

1 12

2 2

A

A

4

1 1

2

A

A A1 : A2 = 2 : 1

A-2. Imax = 21 2 = 24 = 9I.

Imin = 21 2– = 24 – = I.

[k.M (B) B-1. foi;kZl lEHkkO; vf/kdre rhozrk o lEHkkO; U;wure rhozrk dk vuqikr n'kkZrk gSA

As max

min

=

2

1 2

2

1 2–

vr% ;g dsoy L=kksr rhozrk ij fuHkZj djrk gSA

B-2 w = D

d

paqfd v = f

pqafd fuokZr mifLFkr gS, c<+rk gS fÝat pkSM+kbZ c<+rh gSA

B-3. Kkr gS fd =D

d

& vksj yellow > blue.

?kVus ij Hkh ?kVsxk

B-4. pwafd << d; Kkr gS fd = D

d

izkIr gksxk = 9

3

500 10 1

10

= 0.5 mm.

pwafd vR;Yi ugh gS vr% ,slk gks ldrk gS fd 1000th mfPp"B rd ge y’ = 1000 × . iz;qDr uk dj lds ns[krs gS fd ge iz;qDr dj ldrs gS D;k &

1000th mfPp"B ij iFkkUrj = 1000 .

Wave Optics




1000 = d sin =2 2

d y

D y

(5 × 10–4)2 = 3 2 2

2 2

(10 m) y

D y

0.25 D2 = y2 (1 – 0.25) y =

1

20.25D

0.75

y = D

3 = 0.577 m.

pwafd 0.577 m. o 0.5 m. i;kZIr nwfj;k¡ gS] vr% ge bl izdkj dh Å¡ps mfPp"Bksa ds fy, y’ = 1000 iz;qDr ugha

dj ldrsA

B-5. Lets look at the screen.

tSlk fd ge tkurs gS fd 75% rhozrk 3 0 rhozrk ds fcUnq ds laxr gksxhA

{Imax = 4 I0}

I = I0 + I0 + I I0 02 cos

3I0 = 2I0 (1 + cos )

cos () =

= 3

, 2 –

3

, 2 +

3

,...........

p = 6

, –

6

, +

6

,...........

p = yd

D

3I0

D

yd

D =

6

y =

D

d ×

6

,........

y = 6

, –

6

, +

6

ymin. = 3

y =3

×

D

d =

–10

–3

6000 10 1

3 10

= 0.2 mm

Wave Optics




B-6. Lets take any general point S on the line AB. js[kk AB ij dksbZ fcUnq S fy;k tk;s

Li"Vr% js[kk AB ij S dh fdlh Hkh fLFkfr ds fy, PQS esa :

PQ + QS > PS {fdlh Hkh f=kHkqt esa 2 Hkqtkvksa dk ;ksx rhljh Hkqtk ls vf/kd gksrk gS}

PS – QS < 3. pwafd PS – QS,js[kk AB ij fdlh fcUnq ij iFkkUrj n'kkZrk gS ;g dHkh Hkh 3 ls vf/kd ugha gksxkaA

dsoy 3 5

, ,2 2 2

ds fy, fufEu"B izkIr gksxsaA

vr% R (AB dk e/; fcUnq) ds uhps 3 fufEu"B o Åij Hkh rhu fufEu"B izkIr gksxsaA

B-7._ 2R 0I I cos

2

2x

3

2RI cos

6

0

I 3

I 4

[k.M (C) C-1.

KkrO; gS fd P dsUnzh; mfPp"B gksxk (tgk¡ iFkkUrj 'kwU; gS)

vc OP = d d d

–2 3 6

C-2. pkSFkk mfPp"B y = 4 ij gksxk

y = 4 D

d

as Green > blue. Green > blue XGreen > Xblue

Also get X(blue) 4360

X(green) 5460

Wave Optics




[k.M (D) D-1.

Li"Vr% dsUnzh; mfPp"B P ij (izkjfEHkd) P’ ij foLFkkfir gksxh tgk¡ PP’ = 5 mm.

vr% vc , P’ ij iFkkUrj 'kwU; gksuk pkfg,A

d sin = ( – 1)t d tan = ( – 1)t

= 1 + d.(PP')

Dt ; get izkIr gksxk = 1.2

D-2. ge tkurs gS fd ] 75% rhozrk okys fcUnq ij

cos = 1

2 {lUnHkZ Q B–4, iz'ukoyh –I oLrqfu"B}

2

× P = 3

,5

3

,7

3

,11

3

,13

3

(µ – 1) t = 5 7 11 13

, , , ,6 6 6 6 6

t = 5 7 11 13

, , , ,6( – 1) 6( – 1) 6( – 1) 6( – 1) 6( – 1)

= 0.2 m; 1 m, 1.4 m, 2.6 m....... vr% 1.6 m lEHko ugh gSA

[k.M (E)

E-1. (t1 – t2) (n – 1) = 2

[(t1 + t2)] (n – 1) = 2 3t1 = 5t2 – 1

21

21

tt

)tt(

= 4

1 4t1 – 4t2 = t1t2

= 3t1 = 5t2

= 1

2

t

t =

5

3

x = 15. E-2. fp=k ls ;g Li"V gS fd dsfUnz; mfPp"B dh O ls nwjh D gSA

Wave Optics




[k.M (F) F-1. rhoz ijkorZu ds fy,

2t = 3 5

, ,2 2 2

......

= 4t, 4 t 4 t 4 t

, ,3 5 7

......

3000 nm. 1000 nm, 600 nm, 430 nm, 333 nm. dsoy 600 nm lgh fodYi gSA

[k.M (G)

G-2. 1.22λ

dθa

G-3. tc v/kzqohr izdk'k ikSysjkbM+ ls xqtjrk gS] rc bldh rhozrk 50% gks tkrh gSA

G-4. a

Rv Rv

G-5. cszosLVj fu;e ds }kjk ijkofrZr izdk'k }kjk lery /kzqohr izdk'k gksxk rFkk vkiru ry ds yEcor~ gksxkA

G-6. D

mm1

a22.1

a = 3mm, = 500nm

G-7. a

=

D

R

rFkk x-Ray < visible Rx-Ray< 0.1

Hkkx - III 1. dsUnzh; mfPp"B ls nwjh x ij insZ ij rhozrk gS&

I = I0 + 4I0 + 0 02 4 cos2 x

, tgk¡ =D

d

Imax = 9I0 and Imin = I0

(A) tgka rhozrk vf/kdre rhozrk dh 1

9th gS ogk¡ fufEu"B curk gSA

mu fcUnqvksa ds e/; nwjh , 2, 3, 4, .....

(B) tgk¡ rhozrk vf/kdre rhozrk dh 3

9th gS ogka cos

2 x

= –1

2 or x =

3

.

bu fcUnqvksa ds e/; nwjh 2

,3 3

, , +

3

, +

2

3

, 2, .....

(C) cos 2 x

= 0 or x =4

.

bu fcUnqvksa ds e/; nwjh 2

, , +

2

, 2, .....

Wave Optics




(D) cos 2 x

= 1

2 or x =

6

.

bl izdkj ds fcUnqvksa ds e/; nwjh 2

,3 3

, , +

3

, +

2

3

, 2, .....

2. fcUnq P dk y-funsZ'kkad = D

2d

= fÝUt pkSM+kbZ dh vk/khA vr% fcUnq P ij izkjfEHkd rhozrk 'kwU; gSA

(A) d dks nqxquk djus ij fÝUt pkSM+kbZ vk/kh gks tkrh gSA ifj.kke Lo:i izFke Js.kh pedhyh fÝUt P ij cusxh rFkk

fcUnq P ij v/;kjksfir rjaxksa ds chp izdk'kh; iFkkUrj c<+ tk;sxkA

(B) D dks nqxquk djus ij] fÝUt dh pkSM+kbZ nqxquh gks tk,xh vr% fcUnq P ij rhozrk 'kwU; ugh gksxh( fcUnq P ij

rjaxksa dk izdk'kh; iFkkUrj ?kV tk,xkA

(C) fLYV dh pkSM+kbZ de djus ij S1 ls ÅtkZ de gks tk;sxhA ijUrq D dks nqxquk djus ij P ij rhozrk 'kwU; ls

v'kwU; gks tk;sxhA vr% lHkh B fLFkfr dh rjg gSA

(D) ;fn fudk; dks 4

3 viorZukad xq.kkad okys ikuh esa Mqcks fn;k tk, rks fÝUt dh pkSM+kbZ de gks tk;sxh] izdk'kh;

iFkkUrj igys dk 4

3 gks tk,xkA vr% P ij dkyh fÝUt ugh cusxh blfy;s P ij rhozrk c<+sxhA

Wave Optics

Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.) - 324005



Hkkx - I

1. max min

max min

–

=

2 2

1 2 1 2

2 2

1 2 2 2

– –

–

= 1

1

×

2 2

2 2

1 1

2 2

2 2

1 1

1 – 1–

1 1–

= 2 2

2 2

(1 2) – (1– 2)

(1 2) (1– 2)

= 8 4

10 5

2. LiVr% = 1 ds fy, O mfPp"B gS c<+us ij rhozrk ?kVsxh vr% fodYi (C) lgh gSA 3. ekuk 400nm dk nth fufEu"B 600nm ds mth fufEu"B ds lEikrh gSA

1

n2

D400

d = =

1m

2

. D

600d

400 n = 600m + 100.

n = 6m 1

4

= (some integer or non-integer) + 0.25

vr% n dHkh Hkh iw.kk±d ugha gksxk] vr% 600 nm dk dksbZ Hkh fufEu"V 400 nm ds fdlh Hkh fufEu"V ls lEikrh ugha

gksxkA 4. D dh rqyuk esa d vR;Yi ugha gS vr% p = d siniz;qDr ugha dj ldrs

S1P – S2P = P =2

{ izFke fuEu"B}

2 25 12 – (12) = 2

get = 2 cm

5. At B; P = 4 (mfPp"B)

At x = ; P = 0 (mfPp"B)

vr% og fcUnq ftuesa iFkkUrj , or 2 or 3 os mfPp"B gksxsA vr% 3 mfPp"B izkIr gksxsaA

Wave Optics




6. (c)

s1 s2

d

x dcos n

d 2

n

cos2

n 1

1

cos2

60 7. tc izdk'k viorZukad ds ek/;e ls xqtjrk gS] rks izdk'k iFk (t) gksxkA vr% O ijgq¡pus ds igys S1 dk izdk'k (l + b) nwjh pysxk o S2 dk izdk'k (l + b) nwjh pysxkA

i.e. : iFkkUrj = (l + b) – (l + b) = ( – 1) l. NksVs vo;o 'dx' ds fy, iFkkUrj x = [(1 + ax) – 1] dx = ax dx

dqy yEckbZ ds fy, ;

x = 2

O

aax dx

2

'O' ij fufEu"B ds fy,

x = (2n + 1) 2

i.e. : 2a

2

= (2n + 1)

2

.

'a' ds U;wure eku ds fy, n = 0

2a

2 2

a =

2

Ans.

Wave Optics




8. nks L=kksr gSA

O ij mfPp"B gS vr% OP =

d .D

2 (3d)

; get

23d

2D

9. fcUnq O fufEu"B gS vr% izFke mfPp"B O ls y =2

ij gksxkA

y = D

2(2d)

=

–9

–3

600 10 1

4 1 10

= 0.15 mm.

10. A B

C D

P ij izFke vnhIr fÝat ds fy,

A

B

C

D

P

also C ~ B A – D = 2 11._ a sin 30° = a = 2

Wave Optics




Hkkx - II 1.

ekuk 'y' }kjk fufnZ"V {ks=k esa ‘n’ fÝats gS

y = n = n. D

d

y 0.06 n

tan(0.06º )D 180 d

n =310

0.06180

=

3

> 1.

vr%] fcUnq O ds Åij o uhps ,d&,d mfPp"B gksxkA bl izdkj dqy 3 pedhys fcUnq mifLFkr gksaxs (tgk¡ fcUnq ‘O’

ij dsUnzh; mfPp"B gksxk) 2.

(i)

Q, s1 o s3 nksuksa ls leku nwjh ij gSA

S1 o S3 ls vk jgs izdk'k ds dkj.k ifj.kkeh vk;ke AR = 2A Q ij ifj.kkeh vk;ke

AR = 3A

23A = (2A)2 + A2 + 2 2A × A cos

3A2 = 5A2 + 4A2 cos

–1

2 = cos, = 2

3

,

4

3

x = 2 2D d – D

= D 2

2

d1 –1

2D

=

2d

2D

2d

2D × 2

=

2

3

max ds fy,

Wave Optics




= 23d

2D

(ii) Intensity for point 'P'

for S1 and S2 at P = 2d 2 2

. 1202D 3

for S1 and S3 at P = 22.d 2 8

. 4802D 3

Again Area = 2 2 2A (2A) 2A cos120 = 3 A

IP = 3I

120°

A

2A=A+A

3. tgk¡ Z = D

2d

=

2

OS4 =

4

n'kkZ;s vuqlkj

;fn P ij rhozrk gS rks S3 o S4 ij izdk'k dh rhozrk /4 o /4 gSA

iFkkUrj S4P – S3P = 0

vr%, fLyV S1 o S2 dh rhozrk

at S4 S4 ij

Wave Optics




p = yd

D =

d z

D 2

= 4

= 2

.4

= 2

4

= R = 1 + 1 + 1 12 cos

2

1 = 2 = 8

S1 o S2 dh rhozrk

If z = D4.

d

= 4

p = yd

D= z d

.2 D

= 4 D 1 d

d 2 D

= 2

= 2

.2d = 4

3 = 4 = 2

cos48 8 8 2

at 'p' ij p = 2 . cos0º2 2 2 2

p = 2. 4. iznf'kZr fp=k ijkorZu o viorZu rhozrk n'kkZrs gSA

vr% O;frdj.k izdk'k 1 o 2dh rhozrk,sa 0

4

o 09

64

gksxh

min

max

=

2

0 0

2

0 0

9–

4 64

9

4 64

=

2

2

1 3–

2 8

1 3

2 8

= 1

49

Wave Optics




5. 1 = 1.4, 2 = 1.7 rFkk ekuk t dk¡p dh ifV~Vdk dh eksVkbZ gSA

dk¡p dh ifV~Vdk ds dkj.k O ij iFkkUrj

1

2

S1

S2

O

6 Minimath

5 Minimath

x = ( 2 – 1 ) t = ( 1.7 – 1.4 ) t = 0.3 t .......(1) vc 5th mfPp"B ( iwoZ) O ds uhps gS rFkk 6th fuEuf"B O ds Åij gSA

iFkkUrj 5 rFkk 5 + /2 ds chp gksxkA

vr% ekuk x = 5 + .......(2)

tgk¡ < / 2

x iFkkUrj ds dkj.k O ij dykUrj

= 2

x = 2

( 5 + ) = 10 +2

. ) .......(3)

fn;k gS O ij rhozrk3

4 Imax vr%

I () = Imax cos2

2

3

4 Imax = Imax cos2

2

;k 3

4 = cos2

2

.........(4)

lehdj.k (3) rFkk (4) ls ge izkIr djrs gaS

= / 6 vFkkZr~ x = 5 + / 6 = (31 / 6) = 0.3 t

t = 31

6(0.3)

=

10(31)(5400 10 )

1.8

m

;k t = 9.3 × 10-6 m = 9.3 m Ans. (14)

Hkkx – III

1.* =

2

1 2

2

1 2

9

1–

fodYi tkap us ls : 1 = 4 unit. 2 = 1 unit.

vksj 1 1

2 2

A

A

= 2.

Wave Optics




2. As d << D, path difference = d sin (at 0) = 1mm × sin 30º = 0.5 mm if it is a maxima 10–3 × 0.5 = (5000 × 10–10 )m × (n) n must be integer. get n = 1000. Hence O is a maxima of intensity 4I0 vc

vc Q ij iFkkurj = d sin only QS1 QS2.

d sin = 1 × 1/2 = 0.5 mm = dk iw.kZ xq.kt] vr% mfPp"B

3. ;fn 'ors izdk'k iz;qDr djsa rks dsUnzh; fcUnq lHkh o.kksZ ds fy, mfPp"B gksxsa vr% ;g 'osr fn[ksxkA

D

d

; pwafd v U;wure gSa

vr% 'osr ds ckn izFke mfPp"B csaxuh o.kZ dk gksxkA

vr% dksbZ vnhIr fÝat ugha gksxh D;ksafd fdlh fcUnq ij lHkh o.kksZ dk fufEu"B izkIr djuk lEHko ugha gSA

4. for = 30º; P = d sin 30º = (150 m) × 1

2 = 75 m.

= 75 × 2

= 8

6

275

3 10

10

= 2

Ires = I + I + 2I cos () = 2I

where I = 0

4

{ maximum intensity = I0 = 4I} Ires = 0

2

= 0º will automatically correspond to central maxima.

= 90º will correspond to path diff = d. = 150 m = 8

6

150 2

3 10

10

=

minima Hence intensity will be 0 at = 90º. 5.

Li"Vr% Q ij iFkkUrj = d sin

b sin btan b.y

d =

2b

2d

tc Hkh 2b

2d ,

2

dk fo"ke xq.kt gksxk rc fcUnq Q ij mu ds fy, fufEu"B gksxkA

Wave Optics




2b

2d =

2

, 3

2

,

5

2

....

= 2b

d ,

2b

3d,

2b

5d .....

Hkkx - IV 1. rjaxkxz ct f=kT;k ds xksyh; lajpuk ds gSA

vr% (D). 2.

rjaxkxz ges'kk çdk'k rjaxksa ds yEcor~ gksrs gSA 3. LuSy ds fu;e ls

0sin(45 ) 2

sinr 1 sinr =

1

2 r = 300

vr%, (B) lgha gSA uksV : fn[kkbZ xbZ js[kk,sa rjaxkxz gS fdj.k ughaA 4. niZ.k ls ijkorZu ds i'pkr~ lekUrj fdj.k Qksdl ij dsfUnzr gksrh gSA

vFkkZr~ lery rjaxkxz Qksdl ij bdV~Bk gksus okys xksyh; rjaxkxz esa ifjofrZr gks tk,xkA

5. In ABC ; sin (i) = 2

d In xyz ;

sin (r) = 1

d

sin i

sin r= 2 = .

Wave Optics




6. If phase difference at point P is zero then n1 d sin = n2 d sin'

dsin

dsin

yP

' = 37°

and as tan' = y

D y = –

3

4m

It is negative because upper path in medium n2 is longer than lower path in the same medium. 7. Path lengths in medium 2 are equal for point O. Therefore path difference = d sin

1n 0.3 mm,

2n

4(0.3)

30.36 mm

109

4dsin

3p10

9

,

=2p

2 1 4 / 3

14 / 3 2 10 / 9

0.310 / 9

= 10

3

= 0 + 0 + 20 4

cos 23

= 0

8. tc ge fcUnq O ls Åij tk;saxs iFkkUrj c<+sxkA O ij iFkkUrj 3 +3

gS vkSj tc ;g 4, gks tkrk gS ogk¡ mfPp"B

gksxkA ek/;e 2 esa mRiUu vfrfjDr iFk fuf'pr :i ls 2

3

dykUrj ls vf/kd gksxkA

a

2

. d sin1. n2 = 2

3

sin1 = 3

25 (dk ç;ksx djus ij) tan 1 =

3

616 =

y

D

y = 300

2 154cm =

150

154cm

Wave Optics




Hkkx - I 1.

rjaxkxz ¼fdj.k ds vfHkyEc½ lekUrj gSA vr% fdj.ksa Hkh lekUrj gksuh pkfg;sA 2. c rFkk d leku rjaxkxz ij gSA

vr% , C = d

rFkk e = f

d – f = c – f D xyr gSA

d – c = 0 f – e = 0 vr% nksuksa cjkcj gksus pkfg;sA 3. fdj.ksa vfHkyEc dh rjQ eqM+ jgh gSA

vr%, ek/;e 1 fojy gksuk pkfg;s rFkk ek/;e 2 l?ku gksuk pkfg;sA

vr%, V1 > V2 . 4. ;fn d = , rc vf/kdre iFkkUrj ls de gksxk blfy;s insZ ij dsoy dsUnzh; mfPp"B gksxkA

;fn < d < 2 rc iFkkUrj 2 ls de gksxk

iFkkUrj x = ls lEcaf/kr insZ ij nks vkSj mfPp"B gksaxsA

vr% (A) rFkk (B) lgh gksaxsA

tc nksuksa fLyV dh rhozrk leku gksxh dkyh fÝUt dh rhozrk 'kwU;

gksxhA izkjfEHkd rhozrk nksukssa fLyV dh leku ugha gSA vr% dkyh fÝUt ij dqN pedhykiu gksxk vr% tc nksuksa dh

rhozrk leku gksxh rks dkyh fÝUt dh rhozrk insZ ij de gksdj 'kwU; gks tk;sxhA vr% (C) rFkk (D) xyr gSA Ans. (A) and (B)

Wave Optics




5. (A) (P1) = 1 + 2 + 2 1 2 cos 2

4

= 0 + 0 + 20 . 1

2= (2 + 2 ) 0

(P2) = 1 + 2 + 20 . 1

2 = 2 1 2 . cos

2

3

= 0 + 0 + 20 . 1

2

= 0

(P1) > (P2)

(B) (P0) = ( – 1)t . 2

= 2

.4 2

(P1) = 2

( 1)t . 04

(P2) = 2

( 1)t .3 6

(P0) = 1 + 2 + 2 1 2 . cos (P0)

= 0 + 0 + 20 . cos 2

=20 (P0) = 40

(P2) = 0 + 0 + 2 0 cos 6

= (2 + 3 )0

(C). (P0) = ( – 1)t . 2

= 2

.2

(P1) = 2 2

( 1)t.4 2

(P2) = 2

( 1)t .3 6

(P0) = 2 2

.2 3 6 3

(D) (P0) = 3 2 3

4 2

(P1) = 0 (P2) > 0, (P0) > 0

6. = D

d

VIBGYOR

c<+sxk

R > G > B So R > G > B

Wave Optics




7. vf/kdre rhozrk dh vk/kh ds fy,

20= 0 + 0 + 20 cos

(dykarj) =3 5

, , .........2 2 2

iFkkarj 3 5 2n 1

, , .........4 4 4 4

8. 2d sin =

d = 2sin

vodyu djus ij

(d)= 2

(cosec)

(d) = (– cosec cot )2

(d) = 2

– cos

2sin

tSlkfd = c<sxk 2

cos

2sin

?kVsxk

Alternate solution

d2sin

n d n n 2 n sin

(d)

d

= 0 – 0 –

1cos ( )

sin

fHkUukRed =kqfV |+(d)| = |cot |

fujis{k =kqfV d = (dcot)

d cos

2sin sin

2

cosd

sin

9. = D

d

2 > 1 vr% 2 > 1

nh xbZ pkSM+kbZ (m) esa fÝUtksa dh la[;k = m2 < m1

2 dk 3rd mfPp"B = 23 D 1800 D

d d

1 dk 5th fufEu"B = 19 D 1800 D

2d d

vr% 2 dk 3rd mfPp"B 1 ds 5th fufEu"B ls feysxk

dks.kh; i`FkDdj.k = d

dks.kh; i`FkDdj.k 1 ds fy;s de gksxk

Wave Optics




10. For constructive interference x = m

4

32 2d x – 2 2d x = m

1

32 2d x = m

x2 = 9m2 2 – d2 p = 3 11. F;ksjh ds vk/kkj ij fÝUtsa v)Zo`Ùkkdkj gksaxh

rFkk 2

11000

d

0 ij x = 2

1000

vr% 0 ij ;g dkyh gksxh

12.

P1

P2 S2 S1

d

dsin

x=dsin

= 600 nm

P1 ij x = 0

P2 ij x = 1.8mm = n

mfPp"Bksa dh la[;k = n = x

= nm600

mm8.1 = 3000

P2 ij x = 3000

vr% pedhyh fÝat cusxh

P2 ij 3000th mfPp"B curk gS.

Wave Optics




'D' fodYi ds fy;s

x = dsin

dx = dcos.d

R = dcos.Rd

Rd =

cosd

R

tSls gh P1 ls P2 dh rjQ xfr djrs gSa rks

cos Rd

Hkkx - II

1. dykUrj = 2

× iFkkUrj

i.e = 2

× 6

=

3

As I = Imax cos2 2

max

= cos2 2

0

= cos2 6

0

= 3

4

3. iaqt uk vfHklkfjr] uk vilkfjr gS] vr% rjaxkxz leryh; jgsxkA 4. = 0 + 2 ()

r

tSlk fd fn;k x;k gS fd f=kT;k c<+us ls rhozrk ?kV jgh gS rFkk ?kVus ls µ Hkh ?kV jgk gSA

rFkk V = C

izdk'k pky csyu ds v{k ij U;wure gksxhA 5. x1 = 0 = 0º 1 = 0 + 0 + 20 cos0º = 40

x2 = 4

Wave Optics




= 2

.4

= 2

2 = 0 + 0 + 20 cos 2

= 20

1

2

= 0

0

4

2

=2

1 .

6. dyk lEcU/k L=kksr ds fy,

1 = 40 dyk vlEcU/k L=kksr ds fy,

2 = 20

0

2

=2

1 .

7. vkdk'k ds LoPN uhys Hkkx ls çdk'k rhozrkvksa esa mrkj rFkk p<+ko n'kkZrk gSA tc ?kwers gq, /kzqod ls ns[krs gSA

8. S1 : tc çdk'k l?ku ek/;e ls ijkofrZr gksrk gS rc dk dykUrj gksrk gSA

S2 : dsUnzh; mfPp"B ;k fuEfu"B ysUl dh eksVkbZ ij fuHkZj djrk gSA

9. ;g ledsUnzh; o`Ùk gksaxsA Ans (4)

10.

IA cos230° = IBcos2 60° A 3

4= B .

1

4

A

B

1

3

Wave Optics




11.

fdj.k 2, fdj.k 1 dh rqyuk esa rsth ls xeu djsxhA

vr% fdj.k iaqt Åij dh rjQ eqM+ tk;sxkA

12.

fcuk p'esa dh vkW[k ds fy, foHksnu dks.k %

1.22D

–9

–2 –2

y 1.22 500 10

25 10 0.25 2 10

y = 30 × 10–6 m = 30 m

13. b /kCcs dh f=kT;k

b = a + a

L

T;kferh; foLrkj + foorZu ds dkj.k foLRkkj

da

db = 0

1 – La2

= 0 a2 = L a = L

bmin. =

L

LL

bmin. = L2

bmin. = L4

14. 4

9

1105

5.110650

d

D

= 650 × 0.3 × 10–5 = 1.95 mm

4

9

2105

5.110520

= 520 × 0.3 × 10–5 = 1.56mm 41 = 52 = 7.8 mm

Wave Optics




15.

I

A C B

I/2

I/2 cos2

B

I/2 cos2 cos2

I

2cos2 =

I

8

cos2 = 1

4

cos = 1

2 = 45°

6.

30° 30°

Central maxima

Slit

v)Zdks.kh; pkSM+kbZ = 30°

asin = asin30° =

fÝat pkSM+kbZ D

d

=

asin30 D

d

6

2

110 0.5

210d

d = 5510

2 = 25m

Wave Optics




fo"k;kRed iz'u ¼SUBJECTIVE QUESTIONS½

1. o ds eku fn;s x;s gS D;skafd JEE ds okLrfod iz'u i=k esa ‘b’ o ds eku ij vk/kkfjr nks vU; iz'u iwNas x;s

Fks] fdUrq rhozrk Kkr djus ds fy, gesa budh vko';drk ugha gS

fdj.k 2 dk iFk n'kkZ;k x;k gS] Li"Vr% buds e/; iFkkUrj gS

PQ – RS = (PS) cos(90–r) – .d tan = (PS) sin r – d tan. Lusy ds fu;e ls

sin = 1. sin r. and PS = d

cos

gesa iFkkUrj izkIr gksxk = d sin

cos

– d tan = 0 .

vr% mfPp"B ij rhozrk 9I gksxh

2. pwafd << d, = D

d

iz;qDr fd;k tk ldrk gS

fufEu"B ds fy,

(a) y = 1

n2

.= 1

n2

D

d

= –3 –3 61.5 10 1 10 1.5 10

11 n1 n22

n = 1, = 2

3 × 1.5 × 10–6 = 1000 nm

n = 2, =2

5 × 1.5 × 10–6 = 600 nm

n = 3, = 2

7 × 1.5 × 10–6 = 428 nm

‘n’ dk iw.kk±d eku j[kus ij

n = 1 ; = 1000 nm n = 2; = 600 nm. n = 3; = 428 nm vr% fNnz ij dsoy = 428 nm rFkk = 600 nm ds fy, fuEu"V izkIr gksxk vr% fuxZr izdk'k ls ;g vuqifLFkr

jgsxsaA

(b) 1.5 mm = n .

1.5 mm =D

n d

= 3 3

2

1.5 10 1 10

n 100 10

Wave Optics




n = 1 ds fy, = 1500 nm

n = 2 ds fy, = 750 nm.

n = 3 ds fy, = 500 nm.

vr% dsoy = 500 nm dh vf/kdre rhozrk gksxhA

3. (a) Li"Vr% 3rd nhIr fÝat y = 3 ij gksxh

= 3 D

d

=

–10

–3

3 (6500 10 ) 1.2

2 10

= 0.117 cm. = 1.17 mm.

(b) 6500Å dh mth nhIr fÝat 5200 Å dh nth nhIr fÝat ds lEikrh gSA

n1 = m2

n

m =

5

4

vr%] U;wure nwjh ds fy, 5200Å dh 5th nhIr fÝat 6500Å dh 4th nhIr fÝat ds lEikrh gksxhA

y’ = 4 1 =–10

–3

4 (6500 10 ) 1.2

2 10

= 0.156 cm = 1.56 mm

4.

O ij iFkkUrj

= dsin tgk¡ n'kkZ;k x;k dks.k gS ¼pwafd >> d)

blfy, P= d sin d tan d.d/ 2

=

2d

2

= 22 d

2

=

2d

.

(a) vc]n'kkZ;s vuqlkj ;fn nzo Hkjk tk;s

iFkkUrj = (SS2 – SS1) + S2 P – S1 P

= 2d

2 +

2d

2D

Wave Optics




dykUrj = 2d 2

2

+ 2d 2

2D ( / )

= 2d 1

D

(b) (i) ;fn cka;h vksj nzo Hkjk tk;s

=2d 2

2 /

+ 2d 2

2D

= 2d

1

D

(ii) Li"Vr% /2 ds ckjs esa iwNk tk jgk gS { << d}.

Dmin = D

2 2d

5.

fdlh ,d f>jhZ (fLyV) o insZ ds chp iryh ifêdk j[kus ij (P = ( – 1) t ) dk vfrfjDr iFkkUrj cu tkrk gS

vr%

S1O – S2O = (– 1) t = 0.75 × 10–6 m

( – 1)t

=

3

2 ( – 1)t =

3

2

fcUnq O O;frdj.k fufEu"V gksxh vr% O dh rhozrk 'kwU; gksxh

S2P – S2P = mdy

D

S2P – S1P = mdy

D– ( – 1)t

dsUnzh; mfPp"B ds fy, O;frdkjh fdj.kksa ds chp iFkkUrj 'kwU; gksrk gS i.e. S2P – S1P = 0

mdy

D = ( – 1)t

ym = D

d ( – 1)t =

4

1

5 10 ×0.75 × 10–6 = 1.5 mm

vr%] fdlh fLyV ds lEeq[k iryh fQYe ¼ijr½ j[kus ij dsUnzh; mfPp"B dk fLyV dh vksj foLFkkiu dk izHkko

mRiu gksrk gSA

Wave Optics




6. Li"Vr% initial = i

D

d

0.25 × 10–3 = d

× 1 m

d

= 2.5 × 10–4 .............(1)

i'pkr~ :

i

2

3 =

D

(d d)

d d

= 42 2.5 10

3 1

.............(2)

(1) dks (2) ls foHkkftr djus ij

d d

d

=

3

2 d = 2 (d) = 2.4 mm.

& = 2.4 × 2.5 × 10–7 m = 600 nm.

vc

vr% P dsUnzh; mfPp"B cu tkrk gS

fcUnq P ds fy, : d sin = ( – 1) t

d. 20

D

tan ( – 1)t

d = ( – 1)t

d 20 D

D d

= (1.5 – 1)t

t = 20

0.5

=

–920 600 10

0.5

= 24 m.

7. (a) B dh vf/kdre eksVkbZ ds fy, dsUnzh; mfPp"B O ds Bhd Åij gksxk

O ij dykUrj =2

3

gksuk vko';d gSA { cos = –

1

2 rhozrk 3I ds fy,}.

O ij iFkkUrj =2

3 2

=

3

d sin 30 + (A – 1) × tA – (B – 1) tB = /3 ls izkIr gksxk tB = 120 m.

(b) vc tB = 120 m.

= D

d

= –10

–3

6000 10 1

0.1 10

= 6 mm.

Imax = 24 = 9 I

Imin = 24 – = I

Wave Optics




(c) 'O' ij iFkkUrj gS P

P = dsin + (A –1) tA – (B – 1) tB 0.1 sin30º + (1.5 – 1) × 20.4 – (1.5 – 1) × 120 P = 2 × 10–7 m

y d

D= P

y = D

Pd =

–3

1

0.1 10 × 2 × 10–7 = y = 2 mm

=D

d

= 6mm

mfPp"B o fufEu"B ds e/; dh nwjh =2

= 3mm

fudVre fufEu"B dh 'O' ls nwjh = 6

= 1mm

(d) blfy, P1 ij dykUrj

= yd

D ×

2

= –3 –448 10 10

1

×

–10

2

6000 10

= 16 'P1' ij rhozrk

I1 = 4I + I + 22 4 cos (16)

I1 = 9 I 'P2' ij rhozrk

'P2' ij dykUrj

=2

× P

Wave Optics




P = yd

D =

52mm 0.1 mm

1 m

=–10

2

6000 10

× 52mm 0.1 mm

1 m

= 52 3

= 16 + 4/3

I2 = 4I + I + 22 4 cos (16+4/3)

I2 = 4I + I + 22 4 cos (4/3) = 4I + I – 2 × 2I ×

1

2

I2 = 3 I 8. leksÙky ySUl dh oØrk f=kT;k Kkr djrs gS

1 1 1

( – 1) –f R –R

1 3 2

– 110 2 R

R = 10 cm.

vc

ysUl ds fy,

1 1 1

–V –20 10

1 1

V 20

ufydk i`"B ds fy, (R = 10 cm.)

2 1 2 1––

V u R

4 / 3 1 4 / 3 – 1–

V 20 –10

V = + 80 cm.

(b) niZ.k ds fy,

niZ.k ds fy, fcEc 20 cm nwjh ij gS blfy, izfrfcEc 20 cm ij gh gksxkA

u = – 2 f v = – 2f also.

vko/kZu = m = 0

y –v

y u

–y –20

–(1 mm) –20

yI = + (1 mm)

vr% vfUre izfrfcEc leku gksxsa

vr% izfrfcEcksa ds chp nwjh 4 mm gksxhA

Wave Optics




(c) vc] I2 o I4 fÝat izk:i ds 2 L=kksr dh Hkkafr O;ogkj djrs gS

= D

d

=

vD

fd =

(c / ) D

fd

= 8

15 –3

3 10 0.84 3

10 (4 10 )3 4

= 60 m.

9. fn;k gS –

= 600 nm = 6 × 10-7 (ek/;e eas)

d = 0.45 nm = 0.45 × 10-3 m D = 1.5 m dkWp dh ijr dh eksVkbZ t = 10.4 m = 10.4 × 10-6 m

ek/;e dh ijr dk vioZrukad m = 4/3

dkWp dh ijr dk vioZrukad g = 1.5

(a) ekuk dsUnzh; mfPp"B O ls y nwjh ij izkIr gksrk gS] rc

x1 = S

1P – S

2 P =

yd

D

dkap dh ijr ds dkj.k iFkkUrj

x2 = g

m

1

t

dqy iFkkUrj 'kwU; gksxk tc –

x1 = x

2 or

yd

D = g

m

1

t y = g

m

1

t

D

d

ekuks dk izfrLFkkiu djus ij] ge izkIr djrs gS fd

y = 1.5

14 / 3

6

3

(10.4 10 )(1.5)

0.45 10

y = 4.33 × 10-3 m Ans.

(b) O ij x1 = O vkSj x

2= g

m

1

t

dqy iFkkUrj x = x2

blds laxr dykUrj ;k lkekU;r = 2

. x

ekuks dk izfrLFkkiu djus ij

= 7

2

6 10

1.51

4 / 3

( 10.4 × 10-6 ) = 13

3

Wave Optics




vc I () = Imax

cos2

2

I = Imax

cos2 13

6

I =3

4I

max Ans.

(c) O ij : iFkkUrj x = x2 = g

m

1

t gSA

O ij vf/kdre rhozrk ds fy;s

x = n ( ;gka n = 1, 2, 3......)

= x x x

, ,1 2 3

............. vkSj blh rjg vkxs

= 1.5

14 / 3

( 10.4 × 106 m) = 1.5

14 / 3

( 10.4 × 103 nm )

= 1300 nm

vf/kdre rhozrk fuEu ds laxr gksxh

= 1300 nm, 1300

2nm,

1300

3nm,

1300

4nm.........

= 1300 nm, 650nm, 433nm.33nm, 325nm....... 400 ls 700 nm dh ijkl esa rjax nS/;Z

650 nm vkSj 433,33 nm gksxhA

10. vkifrr fdj.k AB vkaf'kd ijkofrZr gksrh gS fdj.k 1 ds :i esa Åijh lrg ls rFkk fdj.k 2 ds :i esa fp=kkuqlkj

viorZu xq.kkad 1 = 1.8 rFkk t eksVkbZ dh ijr dh fupyh lrg ls vkaf'kd ijkofrZr gksrh gS nksuksa fdj.kksa ds e/;

iFkkUrj gksxk&

x = 2 1t = 2 (1.8) t = 3.6 t

fdj.k 1 l?ku ek/;e ls ijkofrZr gksrh gS] vr% blesa dk dyk ifjorZu gks tkrk gS tcfd fdj.k 2 fojy ek/;e ls

ijkofrZr gksrh gS vr% bldh dyk esa dksbZ ifjorZu ugha gksxkA bl izdkj fdj.k 1 o 2 esa = dk dykUrj gksxk

vr% lEiks"kh O;frdj.k dh 'krZ gksxh &

x = 1

n2

,

tgk¡ n = 1,2,3........

;k 3.6 t = 1

n2

t dk fuEure gy n = 1 ds laxr gksxk

;k tmin

= 2 3.6

;k tmin

= 648

7.2nm

;k tmin

= 90 nm

Wave Optics




(i) rjax ds fy, (/ofu ;k oS|qrpqEcdh;) ,d ek/;e l?ku ;k fojy gksxk] ;g ek/;e esa rjax dh pky ls

fu/kkZfjr gksrk gSA l?ku ek/;e esa rjax dh pky de gksxhA mnkgj.k Lo:i ikuh] /ofu ds fy;s fojy ek/;e gS]

tcfd ikuh izdk'k ds fy, ok;q dh rqyuk esa l?ku ek/;e gSA D;ksfd /ofu dh pky ty esa ok;q ds lkis{k T;knk gS

tcfd izdk'k dh pky de gSA

(ii) ikjxeu @ viorZu esa] dyk ifjofrZr ugh gksrh gS] ijkorZu esa tc ijkorZu l?ku ek/;e ls gks rks dyk ifjorZu

gks tkrk gS tcfd fojy ek/;e ls ijkorZu ij dyk ifjofrZr ugh gksrh gSA

(iii) tc nks rajxs tks leku dyk esa gS tc x ds iFkkUrj ds lkFk O;frdj.k djrh gS rks vf/kdre rhozrk dh 'krZ

gksxh

x = n : n = 0,1,2....... ijUrq tc nks rjaxs tks igys ls gh foijhr dyk ¼dykUrj ½ esa gS tc x ds iFkkUrj ds lkFk O;frdj.k djrh gS rks

vf/kdre rhozrk dh 'krZ gksxh

x = 1

n2

: n = 0,1,2,......

hkkx - iwave optics reg. & corp. office: cg tower, a-46 & 52, ipia, near city mall, jhalawar...

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