Magalasi opindika - mavuto ndi mayankho

1. Chinthu chimayikidwa pa 10 cm kuchokera pa galasi lopindika. Utali wa focal ndi 5 cm. Dziwani (a) Chithunzicho mtunda (b) kukula kwa chithunzi

Zodziwika:

Utali wofunikira (f) = 5 cm

Mtunda wa chinthucho (d_o) = 10 cm

Anakonza :

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi:

1/d_i = 1/f – 1/d_o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10

d_i = 10/1 = 10 cm

Mtunda wa chithunzi ndi 10 masentimita.

Kukula:

m = –d_i / d_o = -10/10 = -1

1 imatanthauza kuti chithunzicho ndi chofanana ndi chinthucho.

Chizindikiro chochotsera imasonyeza kuti chithunzicho chasinthidwa. Ngati chizindikirocho chili chabwino ndiye kuti chithunzicho chili choyima.

2. Chinthu cha kutalika kwa masentimita 5 chimayikidwa patsogolo pa galasi lopindika lomwe lili ndi utali wa masentimita 20. Dziwani kutalika kwa chithunzi ngati mtunda wa chinthucho ndi 5 cm, 15 cm, 20 cm, 30 cm.

Zodziwika:

Utali wa kupindika (r) = 20 cm

Utali wofunikira (f) = R/2 = 20/2 = 10 cm

Kutalika kwa chinthucho (h_o) = 5 cm

Yankho:

a) kutalika kwa focal (f) = 10 cm ndi mtunda wa chinthucho (d_o) = 5 cm

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/5 = 1/10 – 2/10 = -1/10

d_i = -10/1 = -10 cm

Chizindikiro chochotsera chikusonyeza chithunzi chimenecho ndi yeniyeni kapena chithunzi chili kumbuyo kwa galasi.

Kukula kwa chithunzi (m):

m =-d_i / d_o = -(-10)/5 = 10/5 = 2

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Kutalika kwa chithunzi (h_i):

m = h_i / h_o

h_i = h_o m = (5 cm)(2) = 10 cm

Kutalika kwa chithunzi ndi 10 cm.

b) Utali wofunikira (f) = 10 cm ndi mtunda wa chinthucho (d_o) = 15 cm

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/15 = 3/30 – 2/30 = 1/30

d_i = 30/1 = 30 cm

Chizindikiro chowonjezera chimasonyeza kuti chithunzicho ndi chenicheni kapena chithunzicho ili 30 cm patsogolo pa galasi, mbali yomweyo ndi chinthucho.

Kukula kwa chithunzi (m):

m =-d_i / d_o = -30/15 = -2

Chizindikiro chochotsera chimasonyeza kuti chithunzicho chatembenuzidwa.

Chithunzicho ndi chachikulu kawiri kuposa chinthucho.

Kutalika kwa chithunzi (h_i):

m = h_i / h_o

h_i = h_o m = (5 cm)(2) = 10 cm

Kutalika kwa chithunzi ndi 10 cm.

c) Kutalika kwa focal (f) = 10 cm ndi mtunda wa chinthucho (d_o) = 20 cm

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi (d)_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/20 = 2/20 – 1/20 = 1/20

d_i = 20/1 = 20 cm

Chizindikiro chabwino chimasonyeza kuti chithunzicho ndi chenicheni kapena chithunzicho ili 20 cm patsogolo pa galasi, mbali yomweyo ndi chinthucho.

Kukula kwa chithunzi (m):

m =-d_i / d_o = -20/20 = -1

Chizindikiro chotsutsa chimatanthauza kuti chithunzicho chatembenuzidwa.

Kutalika kwa chithunzi (hi):

m = h_i / h_o

h_i = h m = (5 cm)(1) = 5 cm

d) Utali wofunikira (f) = 10 cm ndi mtunda wa chinthucho (d_o) = 30 cm

Mtunda wa chithunzi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/30 = 3/30 – 1/30 = 2/30

d_i = 30/2 = 15 cm

Chizindikiro chowonjezera chimasonyeza kuti chithunzicho ndi chenicheni kapena chithunzicho chili pa 15 cm patsogolo pa galasi, mbali yomweyo ndi chinthucho.

Kukula kwa chithunzi (m) :

m =-d_i / d_o = -15/30 = -0.5

Chizindikiro chochotsera chimasonyeza kuti chithunzicho chatembenuzidwa.

Chithunzicho ndi chaching'ono ndi 0.5 kuposa chinthucho.

Kutalika kwa chithunzi (h_i):

m = h_i / h_o

h_i = h_o m = (5 cm)(0.5) = 2.5 cm

3. Chithunzi chopangidwa ndi galasi lopindika chimakhala chachikulu nthawi zinayi kuposa chinthucho. Ngati utali wa kupindika ndi masentimita 20, dziwani mtunda wa chinthucho patsogolo pa galasi!

Zodziwika:

Kukula kwa chithunzi (m= = 4

Utali wa kupindika (r) = 20 cm

Utali wofunikira (f) = r/2 = 20/2 = 10 cm

anafuna : Mtunda wa chinthucho (d_o)

Yankho:

m =- d_i / d_o

4 = - d_{i /} d_o

- d_i = 4 d_o

d_i = – 4 d_o

1/f = 1/d_o + 1/d_i

1/10 = 1/d_o + 1/4d_o

4/40 = 4/4d_o + 1/4d_o

4/40 = 5/4d_o

(4)(4s) = (5)(40)

16 d_o = 200

d_o = 12.5 masentimita

Mtunda wa chinthu = 12.5 masentimita.

4Chinthu cha kutalika kwa 1 cm chimayikidwa 10 cm kuchokera pagalasi lopindika ndi kutalika kwa focal, f = 15 cm. Dziwani:

A. Mtunda wa chithunzi?

B. Kutalika kwa chithunzi?

C. Kodi chithunzi chopangidwa ndi galasi lopindika ndi chiyani?

Zodziwika:

Kutalika kwa chinthu (h) = 1 cm

Mtunda wa chinthu (d)_o) = 10 cm

Kutalika kwa galasi lopindika (f) = 15 cm

Yankho:

A. Mtunda wa chithunzi (d)_i)

1/f = 1/d_o + 1/tsiku_i

1 /d_i = 1/f – 1/d_o = 1/15 – 1/10 = 2/30 – 3/30 = -1/30

d_i = -30/1 = -30 cm

Chizindikiro chotsutsa chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi.

B. Kutalika kwa chithunzi (h_i)

Kukula kwa chithunzi (M):

M = -d_i/d_o = h_i/h_o

M = -(-30)/10 = 30/10 = katatu

Kutalika kwa chithunzi (h_i):

M = h_i / h_o

3 = ola_i / 1 masentimita

h_i = 3 (1 cm)

h_i = 3 masentimita

Kutalika kwa chithunzi ndi 3 cm. Chizindikiro chowonjezera chimasonyeza kuti chithunzicho chili mmwamba.

C. Makhalidwe a chithunzicho:

Zenizeni, mmwamba, zazikulu kuposa chinthu

5. Kukula kwa chithunzicho, malinga ndi chithunzi chomwe chili pansipa.

Zodziwika:

Mtunda wa chinthu (d)_o) = 60 cm

Kutalika kwa focal (f) = 20 cm

Akufuna: Kukula kwa chithunzi (M)

Yankho:

Mtunda wa chithunzi:

1/f = 1/d_o + 1/tsiku_i

1 /d_i = 1/f – 1/d_o = 1/20 cm – 1/60 cm = 3/60 cm – 1/60 cm = 2/60 cm

d_i = 60/2 cm = 30 cm

Kukula kwa chithunzi (M):

M = d_i/d_o = 30 cm / 60 cm = 1/2 nthawi

6. Ngati Chinthucho chayikidwa 6 cm kuchokera pagalasi lopindika, mtunda wa chithunzicho ndi 12 cm monga momwe chithunzi chili pansipa chikusonyezera. Kodi mtunda wa chithunzicho ndi wotani ngati chinthucho chasunthidwa kuchokera pamalo oyamba 1 cm kutali ndi galasi?

Zodziwika:

Mtunda wa chinthu (d)_o) = 6 cm

Mtunda wa chithunzi (d)_i) = 12 cm

Akufuna: ngati mtunda wa chinthucho (d)_o) = 7 cm ndiye mtunda wa chithunzi ndi …

Yankho:

1/f = 1/do + 1/di = 1/6 + 1/12 = 2/12 + 1/12 = 3/12

f = 12/3 = 4 cm

Kutalika kwa focal ndi kwabwino, kutanthauza kuti focal point ndi yeniyeni kapena kuwala kumadutsa mu point.

Mtunda wa chithunzi:

1 /d_i = 1/f – 1/d_o = 1/4 – 1/7 = 7/28 – 4/28 = 3/28

d_i = 28/3 = 9.3 cm

7. Dokotala wa mano amaona ndi kuyang'ana mano a wodwalayo pogwiritsa ntchito galasi lokhala ndi utali wa masentimita 8. Kuti dzenjelo liwoneke bwino kwa dokotala, kodi mtunda pakati pa mano a wodwalayo ndi galasi ndi wotani?

A. zosakwana 4 cm patsogolo pa galasi lopindika

B. zosakwana 4 cm patsogolo pa galasi lozungulira

C. kuposa 4 cm patsogolo pa galasi lopindika

D. kuposa 4 cm patsogolo pa galasi lozungulira

Zodziwika:

Utali wa galasi (r) = 8 cm

Utali wa galasi (f) = r / 2 = 8 / 2 = 4 cm

Akufuna: Mtunda pakati pa mano a wodwalayo ndi galasi

Yankho:

Galasi lomwe limagwiritsidwa ntchito ndi galasi lopindika kapena galasi lopindika? Kuti dzenje la dzino liwonekere bwino kwa dokotala, galasi lomwe likugwiritsidwa ntchito liyenera kukhala lotha kukulitsa chithunzi cha dzino ndipo chithunzicho chiyenera kukhala choyima. Magalasi opindika nthawi zonse amapanga zithunzi zopindika ndipo kukula kwa chithunzicho kumakhala kochepa kuposa kukula kwa chinthucho. Mosiyana ndi zimenezi, galasi lopindika limatha kupanga chithunzi choyima ngati mtunda wa chinthu (d) ndi wocheperako kuposa kutalika kwa focal (f). Ngati mtunda wa chinthucho ndi waukulu kuposa kutalika kwa focal (f) ndiye kuti galasi lopindika limapanga chithunzi chopindika.

Utali wa focal (f) wa galasi lopindika ndi 4 cm, choncho mano a wodwalayo ayenera kukhala ochepera 4 cm kutsogolo kwa galasi lopindika.

Yankho lolondola ndi A.

8. Galasi lopindika lili ndi utali wozungulira wa masentimita 24. Ngati chinthucho chayikidwa patsogolo pa galasi pa masentimita 20, ndiye kuti mudziwe momwe chithunzicho chilili.

A. Zenizeni, zowongoka komanso zokulirapo

B. Zenizeni, zopotoka komanso zokulitsidwa

C. Wowoneka bwino, wowongoka komanso wokulirapo

D. Pakompyuta, yozungulira komanso yaying'ono

Zodziwika:

Radius ya kupindika (r) = 24 cm

Kutalika kwa focal (f) = R/2 = 24/2 = +12 cm

Kutalika kwa galasi lozungulira ndi kwabwino kapena kwenikweni chifukwa kuwala kumadutsa pamalo ozungulira galasi.

Mtunda wa chinthu (d) = 20 cm

Akufuna: Kapangidwe ka chithunzi

Yankho:

Chithunzi ndi chenicheni kapena chenicheni? Werengani mtunda wa chithunzi:

1/d + 1/d' = 1/f

1/d' = 1/f – 1/d

1/d' = 1/12 – 1/20

1/d' = 5/60 – 3/60

1/d' = 2/60

d' = 60/2

d' = 30 cm

Kutalika kwa chithunzi komwe kwalembedwa kuti ndi chabwino kumatanthauza kuti chithunzicho ndi chenicheni chifukwa chadutsa ndi kuwala.

Chithunzi chokulitsidwa? Chowongoka kapena chopotoka? Choyamba werengerani kukula kwa chithunzi (M):

M = -d' / d = -30/20 = -1.5

M > 1 amatanthauza kuti chithunzi chakulitsidwa, M ali ndi chizindikiro chotsutsa amatanthauza chithunzi chosinthidwa. Chifukwa chake mawonekedwe a chithunzicho ndi enieni, osinthidwa, okulirapo.

Yankho lolondola ndi B.

9. Galasi lozungulira limapanga chithunzi chokhala ndi kukula kowirikiza kasanu kuposa chinthu chomwe chili pazenera, mamita asanu kutali ndi chinthucho. Galasi ili…..

A. concave yokhala ndi kutalika kwa focal kwa 25/24 m

B. convex yokhala ndi kutalika kwa focal kwa 25/24 m

C. concave yokhala ndi kutalika kwa focal kwa 24/25 m

D. convex yokhala ndi kutalika kwa focal kwa 24/25 m

Zodziwika:

Kukula kwa chithunzi (M) = nthawi 5

Mtunda pakati pa chinthu ndi chithunzi = mamita 5

Yankho:

Kukula kwa chithunzi chopangidwa ndi galasi lopindika nthawi zonse kumakhala kochepa kuposa kukula kwa chinthucho, chifukwa chake, galasilo ndi galasi lopindika.

Mtunda wa chinthu (d) = x

Mtunda wa chithunzi (d') = x + 5

Kukula kwa chithunzi (M) = nthawi 5

Fomula yokulitsa chithunzi:

Fomula ya kutalika kwa focal (f):

Yankho lolondola ndi A.

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