Фізика, збірник задач

21.6. GZ s•ebgb ijbkljhx Xg‰Z \•^klZgv f•` ydbfb G ff iZ^Z}

fhghojhfZlbqgZ k\•leh\Z o\bey GZ _djZg• sh jhaf•s_gbc gZ \•^klZg• / f \•^ s•ebg \bgbdZ} kbkl_fZ •gl_jn_j_gp•cgbo kfm] H^gm •a s•ebg i_j_djb\Zxlv kdeyghx ieZklbgdhx a ihdZagbdhf aZehfe_ggy n = 1,5 • lh\sbghx • fdf GZ ydm

\•^klZgv û\ af•klylvky •gl_jn_j_gp•cg• kfm]b" ff

21.7. >a_jdZeZ Nj_g_ey hk\•lexxlvky fhghojhfZlbqgbf k\•lehf a

^h\`bghx o\be• fdf J_[jh ^a_jdZe jhalZrh\Zg_ gZ \•^klZg• 5 f \•^ iZjZe_evgh€ ^h gvh]h s•ebgb ydZ } ^`_j_ehf k\•leZ ?djZg jhaf•s_gh gZ \•^klZg• ' f \•^ j_[jZ ^a_jdZe <•^klZgv f•` •gl_jn_j_gp•cgbfb kfm]Zfb gZ _djZg• û[ ff. Ijh-

f_g• iZ^Zxlv gZ _djZg ijb[ebagh i_ji_g^bdmeyjgh <bagZqblb dml . f•` ^a_jdZeZfb Nj_g_ey (0,15760)

21.8.GZ fbevgm ie•\dm ihdZagbd aZehfe_ggy ydh€ n = 1,33, iZ^Z} [•e_ k\•leh i•^ dmlhf  = 450 ^h ih\_jog• ie•\db <gZke•^hd •gl_jn_j_g- p•€ fZdkbfZevgh i•^kbe_gbf [m^_ \•^[bl_ k\•leh a ^h\`bghx o\be•

fdf AgZclb f•g•fZevgm lh\sbgm ie•\db dmin. fdf

21.9. Imqhd fhghojhfZlbqgh]h k\•leZ a ^h\`bghx o\be• fdf iZ^Z} i•^ dmlhf  = 300 gZ fbevgm ie•\dm a ihdZagbdhf aZehf-

e_ggy n = 1,3 sh agZoh^blvky m ih\•lj• AZ ydh€ gZcf_grh€ lh\- sbgb d ie•\db \•^[bl• k\•leh\• o\be• [m^mlv fZdkbfZevgh ihkeZ[e_g• •gl_jn_j_gp•}x" fdf)

21.10. GZ ijhahjm ieZklbgdm a ihdZagbdhf aZehfe_ggy n = 1,45 iZ^Z}

fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be• fdf < ydbo f_`Zo fh`_ af•gx\Zlbkv lh\sbgZ ieZklbgdb sh[ fh`gZ [meh kihkl_j•]Zlb fZdkbfmf m = 12 ihjy^dm ^ey \•^[blbo ijhf_g•\"

fdf fdf

21.11.GZ iehkdhiZjZe_evgm ie•\dm a ihdZagbdhf aZehfe_ggy n = 1,25 ghjfZevgh iZ^Z} iZjZe_evgbc imqhd [•eh]h k\•leZ AZ ydh€ gZc- f_grh€ lh\sbgb ie•\dZ gZcijhahj•rZ h^ghqZkgh ^ey k\•leZ a

^h\`bgZfb o\bev 1 fdf • 2	fdf? fdf
21.12. FhghojhfZlbqg_ k\•leh a ^h\`bghx o\be•				fdf iZ^Z}
ghjfZevgh gZ kdeygbc debg •a	dmlhf ijb	\_jrbg•		Â = 30Ž

91

ff

IhdZagbd aZehfe_ggy kdeZ n = 1,5 <bagZqblb \ •gl_jn_j_gp•cg•c dZjlbg• \•^klZgv • f•` ^\hfZ kmk•^g•fb f•g•fmfZfb ff

21.13.GZ kdeygbc debg ghjfZevgh iZ^Z} fhghojhfZlbqg_ k\•leh Dml f•` ih\_jogyfb debgZ Â = 20Ž IhdZagbd aZehfe_ggy kdeZ n = 1,5. <•^-

klZgv f•` ^\hfZ kmk•^g•fb •gl_jn_j_gp•cgbfb fZdkbfmfZfb m \•^[blhfm k\•le• • ff AgZclb ^h\`bgm k\•leh\h€ o\be• .

fdf

21.14.FbevgZ ie•\dZ ihdZagbd aZehfe_ggy ydh€ n = 1,3 jhaf•s_gZ \_jlbdZevgh • ml\hjx} debg \gZke•^hd kl•dZggy j•^bgb GZ ih\_jo-

gx debgZ ghjfZevgh iZ^Z} fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be• fdf GZ \•^klZg• • ff \bgbdZ} i¶ylv •gl_j-

n_j_gp•cgbo fZdkbfmf•\ m \•^[blhfm k\•le• <bagZqblb dml  debgZ (11,6Ž

21.15. IehkdhhimdeZ e•gaZ jZ^•mk djb\bgb ydh€ 5 f himdehx klhjhghx e_`blv gZ kdeyg•c ieZklbgp• ijbklj•c GvxlhgZ Ijbklj•c hk\•l- ex}lvky fhghojhfZlbqgbf k\•lehf a ^h\`bghx o\be• fdf, yd_

iZ^Z} ghjfZevgh <bagZqblb m \•^[blhfm k\•le• jZ^•mkb ^jm]h]h k\•leh]h • i¶ylh]h l_fgh]h d•e_pv ff ff

21.16.JZ^•mk djb\bgb e•gab m ijbkljh€ ^ey kihkl_j_`_ggy d•e_pv GvxlhgZ

5 f <•^klZgv f•` i¶ylbf • ^\Z^pylv i¶ylbf k\•lebfb d•evpyfb m \•^[blhfm k\•le• • ff AgZclb ^h\`bgm o\be• fhghojhfZlbq- gh]h k\•leZ yd_ ghjfZevgh iZ^Z} gZ ijbklj•c fdf

21.17.Ijbklj•c ^ey hljbfZggy d•e_pv GvxlhgZ hk\•lex}lvky fhghojh-

fZlbqgbf k\•lehf yd_ iZ^Z} ghjfZevgh ^h iehkdh€ ih\_jog• e•gab JZ^•mkb ^\ho kmk•^g•o k\•lebo d•e_pv m \•^[blhfm k\•le• rm

• rm+1 ff JZ^•mk djb\bgb e•gab 5 f <bagZqblb ihjy^- dh\• ghf_jb d•e_pv • ^h\`bgm o\be• k\•leZ fdf

21.18. IehkdhhimdeZ e•gaZ a ihdZagbdhf aZehfe_ggy n = 1,6 himdehx

klhjhghx e_`blv gZ kdeyg•c ieZklbgp• Ijbklj•c hk\•lex}lvky fhghojhfZlbqgbf k\•lehf a ^h\`bghx o\be• fdf JZ^•mk lj_lvh]h k\•leh]h d•evpy m \•^[blhfm k\•le• ^hj•\gx} r3 ff. <bagZqblb nhdmkgm \•^klZgv F iehkdhhimdeh€ e•gab f

92

21.19. Ijbklj•c ^ey kihkl_j_`_ggy d•e_pv GvxlhgZ	hk\•lex}lvky
fhghojhfZlbqgbf k\•lehf a ^h\`bghx o\be•	fdf sh
iZ^Z} ghjfZevgh JZ^•mk djb\bgb e•gab 5 f	JZ^•mk ^jm]h]h
l_fgh]h d•evpy m k\•le• sh ijhcreh q_j_a ijbklj•c r2 ff.
AgZclb ihdZagbd aZehfe_ggy j•^bgb sh aZih\gx} ijhkl•j f•`
e•gahx • kdeyghx ieZklbgdhx (1,4)

21.20. D•evpy GvxlhgZ ml\hjxxlvky f•` ^\hfZ iehkdhhimdebfb e•gaZfb

jZ^•mkZfb djb\bgb R1 f • R2	f yd• ijblbkgml• h^gZ ^h h^gh€
k\h€fb himdebfb ih\_jogyfb Ijbklj•c hk\•lex}lvky fhghojhfZlbq-
gbf k\•lehf a ^h\`bghx o\be•	fdf sh iZ^Z} ghjfZevgh
^h iehkdh€ ih\_jog• e•gab <bagZqblb jZ^•mk r4 q_l\_jlh]h l_fgh]h
d•evpy m \•^[blhfm k\•le• ff

21.21. GZ	ih\_jogx	kdeygh]h h[¶}dlb\Z ihdZagbd	aZehfe_ggy	ydh]h
n1 = 1,5 gZg_k_gZ lhgdZ ie•\dZ ihdZagbd aZehfe_ggy ydh€ n2 = 1,2.
GZ	h[¶}dlb\	iZ^Z} fhghojhfZlbqg_ k\•leh	a ^h\`bghx	o\be•

fdf AZ ydh€ gZcf_grh€ lh\sbgb h ie•\db [m^_ fZdkb-

fZevgbf ihkeZ[e_ggy \•^[blh]h k\•leZ" fdf

21.22.< h^g_ •a ie_q_c •gl_jn_jhf_ljZ FZcd_evkhgZ ^ey \bf•jx\Zggy ihdZagbdZ aZehfe_ggy Zf•Zdm ihf•klbeb \•^dZqZgm ljm[dm ^h\-

`bghx • f D•gp• ljm[db aZdjbeb iehkdhiZjZe_evgbfb kd_evpyfb I•key aZih\g_ggy ljm[db Zf•Zdhf •gl_jn_j_gp•cgZ dZjlbgZ ^ey ^h\`bgb o\be• fdf af•klbeZkv gZ m = 177 kfm] <bagZqblb ihdZagbd aZehfe_ggy n Zf•Zdm (1,00038)

>BNJ:DP1Y K<1LE:

Hkgh\g• nhjfmeb

>bnjZdp•y iZjZe_evgh]h imqdZ k\•leZ gZ h^g•c s•ebg• Z mfh\Z ^bnjZdp•cgbo f•g•fmf•\

a sinϕ = ±2k λ2 , k = 1,2,3, ;

93

[ mfh\Z ^bnjZdp•cgbo fZdkbfmf•\ ih[•qgbo

a sinϕ = ±(2k +1) λ2 , k = 1,2,3, ,

^_ a – rbjbgZ s•ebgb k – ghf_j ihjy^hd ^bnjZdp•cgh]h fZdkbfmfm

ϕ– dml ^bnjZdp•€ λ – ^h\`bgZ k\•leh\h€ o\be•

>bnjZdp•y iZjZe_evgh]h imqdZ gZ ‰jZlp• j_r•lp• Z mfh\Z ]heh\gbo ^bnjZdp•cgbo fZdkbfmf•\

d sinϕ = ±mλ, m = 0,1,2, ,

^_ d = a + b – i_j•h^ ‰jZldb b – rbjbgZ g_ijhahjbo ^•eyghd f•` kmk•^g•fb s•ebgZfb

[ mfh\Z ]heh\gbo ^bnjZdp•cgbo f•g•fmf•\ a sinϕ = ±2k λ2 , k = 1,2, ;

\ mfh\Z ^h^Zldh\bo ^bnjZdp•cgbo f•g•fmf•\

d sinϕ = ± mN λ, m = 1,2, , N −1, N +1, (2N −1), (2N +1) ,

^_ N – aZ]ZevgZ d•evd•klv s•ebg

Jha^•evgZ a^Zlg•klv ^bnjZdp•cgh€ ‰jZldb

R = λλ = mN, m = 1,2, ,

^_ Δλ – gZcf_grZ j•agbpy ^h\`bgb o\bev ^\ho kmk•^g•o ki_dljZevgbo e•g•c (λ i λ+Δλ yd• fh`gZ jha^•evgh kihkl_j•]Zlb m ki_dlj• hljbfZghfm aZ ^hihfh]hx p•}€ ‰jZldb N – aZ]ZevgZ d•evd•klv s•ebg ]jZldb m – ghf_jihjy^hd ^bnjZdp•cgh]h ki_dljZ

22.1. <•^klZgv \•^ ^`_j_eZ k\•leZ a ^h\`bghx o\be• fdf ^h

kn_jbqgh€ o\bevh\h€ ih\_jog• 5	f \•^klZgv \•^ o\bevh\h€
ih\_jog• ^h lhqdb kihkl_j_`_ggy /	f <bagZqblb jZ^•mkb rm

i_jrbo ljvho ahg Nj_g_ey ff ff ff

22.2.<•^klZgv \•^ iehkdh€ o\bevh\h€ ih\_jog• ^h lhqdb kihkl_j_`_ggy

/ f >h\`bgZ o\be• k\•leZ fdf H[qbkeblb jZ^•mkb rm i_jrbo ljvho ahg Nj_g_ey ff ff ff

22.3. <•^klZgv \•^ ^`_j_eZ k\•leZ a ^h\`bghx o\be•		fdf ^h
kn_jbqgh€ o\bevh\h€ ih\_jog• 5	f \•^klZgv	\•^ o\bevh\h€

94

ih\_jog• ^h lhqdb kihkl_j_`_ggy / f AgZclb iehsm ahgb Nj_g_ey fdf2)

22.4. GZ iehkdm ^•ZnjZ]fm a djm]ebf hl\hjhf jZ^•mkhf U ff iZ^Z} \•^ lhqdh\h]h ^`_j_eZ fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be•

fdf >`_j_eh k\•leZ jhalZrh\Zg_ gZ hk• hl\hjm gZ \•^klZg•

5f \•^ gvh]h >ey lhqdb gZ l•c kZf•c hk• hl\•j \•^djb\Z} m = 10

ahg Nj_g_ey <bagZqblb \•^klZgv L \•^ p•}€ lhqdb ^h ^•ZnjZ]fb f

22.5. IehkdZ k\•leh\Z o\bey a ^h\`bghx fdf iZ^Z} ghjfZevgh

gZ ^•ZnjZ]fm a djm]ebf hl\hjhf ^•Zf_ljhf ' ff LhqdZ kihkl_j_`_ggy jhaf•s_gZ gZ hk• hl\hjm gZ \•^klZg• / f \•^ gvh]h Kd•evdb ahg Nj_g_ey \deZ^Z}lvky \ hl\•j ^•ZnjZ]fb" (4)

22.6.JZ^•mk q_l\_jlh€ ahgb Nj_g_ey ^ey iehkdh]h o\bevh\h]h njhglm r4 = 2 ff <bagZqblb jZ^•mk r9 ^_\¶ylh€ ahgb Nj_g_ey ff

22.7.GZ s•ebgm rbjbghx D iZ^Z} ghjfZevgh iZjZe_evgbc imqhd fhghojhfZlbqgh]h k\•leZ a ^h\`bghx o\be• I•^ ydbf dmlhf 3 [m^_ kihkl_j•]Zlbkv ^jm]bc ^bnjZdp•cgbc f•g•fmf k\•leZ" (300)

22.8.GZ s•ebgm rbjbghx a ff iZ^Z} ghjfZevgh fhghojhfZlbqg_

k\•leh a ^h\`bghx o\be• fdf ?djZg gZ ydhfm \bgbdZ} ^bnjZdp•cgZ dZjlbgZ jhaf•s_gbc iZjZe_evgh ^h s•ebgb gZ \•^klZg• / f <bagZqblb \•^klZgv • f•` i_jrbfb ^bnjZdp•c- gbfb f•g•fmfZfb yd• jhalZrh\Zg• ih h[b^\Z [hdb \•^ p_gljZev- gh]h fZdkbfmfm ff

22.9.GZ s•ebgm rbjbghx D ff iZ^Z} ghjfZevgh fhghojhfZlbqg_

k\•leh a ^h\`bghx o\be•	fdf	>bnjZdp•cgZ	dZjlbgZ
kihkl_j•]Z}lvky gZ _djZg• ydbc jhalZrh\Zgbc iZjZe_evgh ^h s•eb-
gb <•^klZgv f•` i_jrbfb ^bnjZdp•cgbfb fZdkbfmfZfb yd• jha-
f•s_g• ih h[b^\Z [hdb \•^ p_gljZevgh]h fZdkbfmfm •			ff.
<bagZqblb \•^klZgv L \•^ s•ebgb ^h _djZgZ f
22.10. GZ ^h\]m ijyfhdmlgm s•ebgm rbjbghx D		fdf i•^ dmlhf

0 ^h €€ ghjfZe• iZ^Z} fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be•

fdf <bagZqblb kbgmkb dml•\ ^bnjZdp•€ sh \•^ih\•^Zxlv

i_jrbf f•g•fmfZf yd• jhaf•s_g• ih h[b^\Z [hdb \•^ p_gljZevgh]h fZdkbfmfm (0,757; 0,657)

95

22.11. GZ ^bnjZdp•cgm ‰jZldm a i_j•h^hf G

fdf iZ^Z} ghjfZevgh

fhghojhfZlbqgZ k\•leh\Z o\bey GZ _djZg• sh \•^^Ze_gbc \•^ ‰jZldb gZ / f \•^klZgv f•` ki_dljZfb ^jm]h]h • lj_lvh]h ihjy^d•\

•ff AgZclb ^h\`bgm o\be• k\•leZ sh iZ^Z} ( fdf)

22.12. GZ ^bnjZdp•cgm ]jZldm a i_j•h^hf G	fdf ghjfZevgh iZ^Z}
k\•leh a ^h\`bghx o\be• fdf AZ ‰jZldhx jhaf•s_gZ a[b-
jZevgZ e•gaZ a nhdmkghx \•^klZggx )	f <bagZqblb \•^klZgv

• gZ _djZg• f•` ki_dljhf lj_lvh]h ihjy^dm • p_gljZevgbf fZdkbfmfhf f

22.13. GZ ^bnjZdp•cgm ‰jZldm ghjfZevgh iZ^Z} imqhd k\•leZ \•^ jha-

jy^gh€ ljm[db M	gZijyfdm dmlZ	^bnjZdp•€ 3	0 a[•]Zxlvky
fZdkbfmfb o\bev	^h\`bghx 1	fdf •	2	fdf

<bagZqblb i_j•h^ d ‰jZldb fdf

22.14. GZ ^bnjZdp•cgm ‰jZldm sh f•klblv N = 500 rljbo•\ gZ ff, iZ^Z} ghjfZevgh fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be•

fdf AgZclb aZ]Zevgm d•evd•klv ^bnjZdp•cgbo fZdkbfmf•\

yd• ^Z} py ‰jZldZ <bagZqblb kbgmk dmlZ 3 ^bnjZdp•€ sh \•^ih\•^Z} hklZggvhfm fZdkbfmfm (7; 0,825)

22.15. GZ ^bnjZdp•cgm ‰jZldm a i_j•h^hf G	fdf i•^ dmlhf	0 iZ^Z}
fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be• gf		FZdkbfmf
ydh]h ihjy^dm [m^_ \b^gh gZ _djZg• ydsh dml ^bnjZdp•€ 3		0? (5)
22.16. GZ ^bnjZdp•cgm ‰jZldm a i_j•h^hf G	fdf • rbjbghx ijhahjh€

qZklbgb . fdf iZ^Z} ghjfZevgh fhghojhfZlbqg_ k\•leh a ^h\`bghx o\be• fdf Kd•evdb fZdkbfmf•\ g_ [m^_ \ ki_dl-

j• ih h^bg [•d \•^ gmevh\h]h fZdkbfmfm ^ey dmlZ 3					0 \gZke•^hd
\ieb\m ]heh\gbo f•g•fmf•\" (2)
22.17. >bnjZdp•cgZ	‰jZldZ rbjbghx	•		f jha^•ey} m ^jm]hfm
ihjy^dm ^\•	ki_dljZevg• e•g•€	a	^h\`bgZfb 1		gf •
2 = 500 gf <bagZqblb i_j•h^ p•}€ ‰jZldb fdf
22.18. I_j•h^ ^bnjZdp•cgh€ ‰jZldb rbjbghx •					f ^hj•\gx}

Gfdf AgZclb j•agbpx ^h\`bg o\bev sh jha^•eyxlvky p•}x

‰jZldhx ^ey k\•leZ a ^h\`bghx o\be•	fdf m ki_dlj•
i_jrh]h ihjy^dm gf

96

IHEYJBA:P1Y K<1LE:

Hkgh\g• nhjfmeb

AZdhg ;jxkl_jZ

tgiB = n21 ,

^_ iB – dml iZ^•ggy ijb ydhfm \•^[blZ k\•leh\Z o\bey ih\g•klx iheyjb-

ah\ZgZ n21 = n2 – \•^ghkgbc ihdZagbd aZehfe_ggy n1

AZdhg FZexkZ

I = I0 cos2 Â ,

^_ I – •gl_gkb\g•klv k\•leZ sh ijhcreh q_j_a ZgZe•aZlhj I0 – •gl_g- kb\g•klv k\•leZ sh iZ^Z} gZ ZgZe•aZlhj  – dml f•` ]heh\gbfb

iehsbgZfb iheyjbaZlhjZ lZ ZgZe•aZlhjZ

23.1.=jZgbqgbc dml ih\gh]h \gmlj•rgvh]h \•^[b\Zggy imqdZ k\•leZ gZ

f_`• j•^bgb a ih\•ljyf ]j = 450 <bagZqblb dml ;jxkl_jZ B ^ey iZ^•ggy ijhf_gy a ih\•ljy gZ ih\_jogx p•}€ j•^bgb (540 44•

23.2.Ijhf•gv k\•leZ yd_ ihrbjx}lvky m ih\•lj• ml\hjx} a ih\_jog_x j•^bgb dml  = 380. <•^[blbc ijhf•gv fZdkbfZevgh iheyjbah\Z- gbc AgZclb dml aZehfe_ggy ijhf_gy (380)

23.3.<•^[blbc \•^ ih\_jog• kdeZ k\•leh\bc ijhf•gv ih\g•klx iheyjb-

ah\Zgbc Dml aZehfe_ggy m kde•	0. <bagZqblb ihdZagbd
aZehfe_ggy kdeZ (1,73)

23.4.Imqhd ijbjh^gh]h k\•leZ iZ^Z} gZ kdeygm ieZklbgdm a ihdZagbdhf aZehfe_ggy n = 1,73 <•^[blbc \•^ kdeZ imqhd k\•leZ ih\g•klx iheyjbah\Zgbc <bagZqblb dml aZehfe_ggy ijhf_gy k\•leZ (300)

23.5.IZjZe_evgbc imqhd k\•leZ i_j_oh^blv a ]e•p_jbgm ihdZagbd aZehf- e_ggy ydh]h n1 = 1,45 m kdeh a ihdZagbdhf aZehfe_ggy n2 = 1,50. <•^[blbc \•^ f_`• ih^•em pbo k_j_^h\bs imqhd klZ} fZdkbfZevgh

iheyjbah\Zgbf AgZclb dml f•` aZehfe_gbf imqdhf • imqdhf sh iZ^Z} gZ ih\_jogx kdeZ (1780)

97

23.6.Imqhd ijbjh^gh]h k\•leZ iZ^Z} gZ ih\_jogx kdeygh€ ieZklbgdb a

ihdZagbdhf aZehfe_ggy n2 = 1,5 ydZ jhaf•s_gZ \ j•^bg• <•^[blbc \•^ ih\_jog• imqhd k\•leZ ih\g•klx iheyjbah\Zgbc • ml\hjx} dml

30 a• kiZ^gbf imqdhf H[qbkeblb ihdZagbd aZehfe_ggy n1

j•^bgb (1,33)

23.7. Imqhd k\•leZ ihrbjxxqbkv \ ih\•lj• iZ^Z} gZ iehkdhiZjZe_evgm

kdeygm ieZklbgdm a ihdZagbdhf aZehfe_ggy n1 = 1,50 gb`gy ih\_jogy ydh€ jhaf•s_gZ m \h^• ihdZagbd aZehfe_ggy ydh€

n2 = 1,30 Imqhd k\•leZ \•^[blbc \•^ f_`• kdeh – \h^Z [m^_ fZdkb-

fZevgh iheyjbah\Zgbf <bagZqblb kbgmk dmlZ iZ^•ggy 1 imqdZ k\•leZ gZ \_jogx ih\_jogx ieZklbgdb. (0,98)

23.8.1gl_gkb\g•klv ijbjh^gh]h k\•leZ sh ijhcreh q_j_a iheyjbaZlhj • ZgZe•aZlhj af_grm}lvky \ Q jZab <bagZqblb dml 3 f•` ]heh\-

gbfb iehsbgZfb iheyjbaZlhjZ • ZgZe•aZlhjZ Ih]ebgZggyf k\•leZ ag_olm\Zlb (450)

23.9. Dml f•` ]heh\gbfb iehsbgZfb iheyjbaZlhjZ	lZ	ZgZe•aZlhjZ
31 = 450 M kd•evdb jZa•\ af_grblvky •gl_gkb\g•klv k\•leZ yd_
\boh^blv a ZgZe•aZlhjZ ydsh dml a[•evrblvky gZ	3	0? (2)

23.10. Ijhf•gv ijbjh^gh]h k\•leZ ihke•^h\gh ijhoh^blv q_j_a iheyjb- aZlhj • ZgZe•aZlhj dml f•` ]heh\gbfb iehsbgZfb ydbo 3 º.

I•^ qZk ijhoh^`_ggy dh`gh]h a g•dhe•\ \ljZlb gZ \•^[b\Zggy • ih]ebgZggy ^hj•\gxxlv ih 5 % •gl_gkb\ghkl• k\•leZ sh iZ^Z} gZ

g•dhev M kd•evdb jZa•\ af_grblvky •gl_gkb\g•klv k\•leZ i•^ qZk ijhoh^`_ggy q_j_a h[b^\Z g•dhe•" (8,86)

23.11. Dml f•`	iehsbgZfb iheyjbaZlhjZ lZ ZgZe•aZlhjZ 3 0 1gl_g-
kb\g•klv	ijbjh^gh]h k\•leZ sh ijhcreh q_j_a lZdm kbkl_fm

af_grm}lvky \ Q jZa•\ G_olmxqb \ljZlhx •gl_gkb\ghkl• k\•leZ i•^ qZk \•^[b\Zggy \bagZqblb m \•^khldZo dh_n•p•}gl k ih]ebgZggy

k\•leZ \ iheyjbaZlhj• lZ ZgZe•aZlhj• (5,7 %)

98

VII D<:GLH<: IJBJH>: <BIJHF1GX<:GGY

L?IEH<? <BIJHF1GX<:GGY

Hkgh\g• nhjfmeb

AZdhg Kl_nZgZ – ;hevpfZgZ

R =σT 4 ,

^_ R* – •gl_]jZevgZ \bijhf•gx\ZevgZ a^Zlg•klv Z[khexlgh qhjgh]h l•eZ σ – klZeZ Kl_nZgZ – ;hevpfZgZ L – Z[khexlgZ l_fi_jZlmjZ Z[khexlgh qhjgh]h l•eZ

AZdhg af•s_ggy <•gZ

λm = Tb ,

^_ λm – ^h\`bgZ o\be• ijb yd•c kihkl_j•]Z}lvky fZdkbfmf \bijh-

f•gx\Zevgh€

a^Zlghkl• Z[khexlgh

qhjgh]h l•eZ b – klZeZ <•gZ

(b = 2,9 10-3 f D

FZdkbfZevgZ \bijhf•gx\ZevgZ a^Zlg•klv Z[khexlgh qhjgh]h l•eZ

(r

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max

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λ,T

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<l

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f3 D 5

NhjfmeZ IeZgdZ

r

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\bijhf•gx\ZevgZ a^Zlg•klv Z[khexlgh qhjgh]h l•eZ k –

ν ,T

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klZeZ ;hevpfZgZ h – klZeZ IeZgdZ

99

24.1.	Ihlm`g•klv \bijhf•gx\Zggy a hl\hjm i_q• iehs_x S		kf2
	^hj•\gx} N <l <bijhf•gx\Zggy [ebavd_ ^h \bijhf•gx-
	\Zggy Z[khexlgh qhjgh]h l•eZ <bagZqblb l_fi_jZlmjm L i_q•
	D
24.2.	AZl_fg_gZ f_lZe_\Z dmey jZ^•mk ydh€ R	kf \ljZqZ} _g_j]•x
	ebr_ \gZke•^hd \bijhf•gx\Zggy L_fi_jZlmjZ dme• L1 D,
	l_fi_jZlmjZ hlhqmxqh]h k_j_^h\bsZ L2	D Ydm ihlm`g•klv

lj_[Z i•^\h^blb ^h dme• sh[ €€ l_fi_jZlmjZ [meZ [•evrhx \•^ l_fi_jZlmjb hlhqmxqh]h k_j_^h\bsZ" <l

24.3. 1gl_]jZevgZ \bijhf•gx\ZevgZ a^Zlg•klv			Z[khexlgh qhjgh]h l•eZ
*	= 30	d<l f2 <bagZqblb ^h\`bgm o\be•
RT			m ydZ \•^ih\•^Z} fZdkb-

fZevghfm agZq_ggx \bijhf•gx\Zevgh€ a^Zlghkl• l•eZ fdf

24.4.<bijhf•gx\Zggy Khgpy aZ k\h€f ki_dljZevgbf kdeZ^hf [ebavd_ ^h \bijhf•gx\Zggy Z[khexlgh qhjgh]h l•eZ fZdkbfmf \bijh- f•gx\Zevgh€ a^Zlghkl• ydh]h kihkl_j•]Z}lvky gZ ^h\`bg• o\be•

m	fdf JZ^•mk Khgpy
ydm \ljZqZ} Khgp_ aZ qZk t

R= 6,95 108 f <bagZqblb fZkm ¨m,

k \gZke•^hd pvh]h \bijhf•gx\Zggy

=d]

24.5.L_fi_jZlmjZ Z[khexlgh qhjgh]h l•eZ a[•evrbeZkv \^\•q• <gZke•- ^hd pvh]h ^h\`bgZ o\be• m ydZ \•^ih\•^Z} fZdkbfZevghfm agZ- q_ggx \bijhf•gx\Zevgh€ a^Zlghkl• af_grbeZkv gZ gf AgZclb ihqZldh\m • d•gp_\m l_fi_jZlmjb l•eZ D D

24.6.<gZke•^hd af•gb l_fi_jZlmjb Z[khexlgh qhjgh]h l•eZ fZdkbfmf

	\bijhf•gx\Zevgh€ a^Zlghkl• (r* ,T)max af•klb\ky a m1		fdf gZ
	m2	fdf M kd•evdb jZa•\ a[•evrblvky •gl_]jZevgZ \bijhf•-
	gx\ZevgZ a^Zlg•klv R*T • fZdkbfZevg_ agZq_ggy \bijhf•gx\Zevgh€
	a^Zlghkl• (r* ,T)max? (81; 243)
24.7.	A ih\_jog• kZ`• iehs_x S kf2 ijb l_fi_jZlmj• L		D aZ
	qZk t	k \bijhf•gx}lvky _g_j]•y W >` <bagZqblb
	dh_n•p•}gl qhjghlb ÂL kZ`• (0,8)
24.8.	L•eh ijb l_fi_jZlmj• hlhqmxqh]h k_j_^h\bsZ Lh D \bijh-
	f•gx} \ jZa•\ [•evr_ _g_j]•€ g•` ih]ebgZ} YdZ l_fi_jZlmjZ
	l•eZ" D
100