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Help the students to determine which mirror forms a bigger image of a man of height 4cm standing 25cm away from each of the mirror. Write a brief report about the nature of image formed by the mirror advise which mirror is suitable for use as driving mirror.

Physics

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Part a· 6 steps

Kuamua kioo kinachounda picha kubwa zaidi

Tutatumia fomula ya kioo na fomula ya ukuzaji kwa kila kioo.
Fomula ya kioo: 1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}
Fomula ya ukuzaji: M=hiho=−vuM = \frac{h_i}{h_o} = -\frac{v}{u}
Ambapo:
ff ni urefu wa focal
uu ni umbali wa kitu
vv ni umbali wa picha
hoh_o ni urefu wa kitu
hih_i ni urefu wa picha

Data zilizopewa:
Urefu wa kitu ho=4 cmh_o = 4 \text{ cm}
Umbali wa kitu u=25 cmu = 25 \text{ cm}
Urefu wa focal wa kioo mbonyeo fconcave=20 cmf_{concave} = 20 \text{ cm}
Urefu wa focal wa kioo mbonyeo fconvex=−20 cmf_{convex} = -20 \text{ cm} (kwa kioo mbonyeo, ff ni hasi)

Kwa Kioo Mbonyeo (Concave Mirror):

  1. Tafuta umbali wa picha (vv).

    120=125+1v\frac{1}{20} = \frac{1}{25} + \frac{1}{v} 1v=120−125\frac{1}{v} = \frac{1}{20} - \frac{1}{25} 1v=5−4100\frac{1}{v} = \frac{5 - 4}{100} 1v=1100\frac{1}{v} = \frac{1}{100} v=100 cmv = 100 \text{ cm}
  2. Tafuta ukuzaji (MM).

    M=−vu=−10025=−4M = -\frac{v}{u} = -\frac{100}{25} = -4
  3. Tafuta urefu wa picha (hih_i).

    M=hihoM = \frac{h_i}{h_o} −4=hi4 cm-4 = \frac{h_i}{4 \text{ cm}} hi=−4×4 cm=−16 cmh_i = -4 \times 4 \text{ cm} = -16 \text{ cm}

    Ukubwa wa picha ni 16 cm16 \text{ cm}. Ishara hasi inaonyesha picha imepinduka.

    Kwa Kioo Mbonyezi (Convex Mirror):

  4. Tafuta umbali wa picha (vv).

    1−20=125+1v\frac{1}{-20} = \frac{1}{25} + \frac{1}{v} 1v=−120−125\frac{1}{v} = -\frac{1}{20} - \frac{1}{25} 1v=−5−4100\frac{1}{v} = \frac{-5 - 4}{100} 1v=−9100\frac{1}{v} = \frac{-9}{100} v=−1009≈−11.11 cmv = -\frac{100}{9} \approx -11.11 \text{ cm}

    Ishara hasi inaonyesha picha ni pepe (virtual).

  5. Tafuta ukuzaji (MM).

    M=−vu=−(−100/9)25=1009×25=49M = -\frac{v}{u} = -\frac{(-100/9)}{25} = \frac{100}{9 \times 25} = \frac{4}{9} M≈0.44M \approx 0.44
  6. Tafuta urefu wa picha (hih_i).

    M=hihoM = \frac{h_i}{h_o} 49=hi4 cm\frac{4}{9} = \frac{h_i}{4 \text{ cm}} hi=49×4 cm=169 cm≈1.78 cmh_i = \frac{4}{9} \times 4 \text{ cm} = \frac{16}{9} \text{ cm} \approx 1.78 \text{ cm}

    Ukubwa wa picha ni 1.78 cm1.78 \text{ cm}. Ishara chanya inaonyesha picha imesimama wima.

    Hitimisho la a):
    Kioo mbonyeo (concave mirror) huunda picha yenye urefu wa 16 cm16 \text{ cm}, wakati kioo mbonyezi (convex mirror) huunda picha yenye urefu wa 1.78 cm1.78 \text{ cm}.
    Kwa hiyo, kioo mbonyeo (concave mirror) huunda picha kubwa zaidi.

Part b

Ripoti fupi kuhusu asili ya picha na ushauri kuhusu kioo cha kuendeshea gari

  • Kioo Mbonyeo (Concave Mirror): Wakati kitu kiko kati ya ff na 2f2f (kama ilivyo katika kesi hii, 20 cm<25 cm<40 cm20 \text{ cm} < 25 \text{ cm} < 40 \text{ cm}), picha inayoundwa ni halisi, imepinduka, na imekuza (kubwa kuliko kitu). Picha huundwa mbele ya kioo.

  • Kioo Mbonyezi (Convex Mirror): Kioo mbonyezi huunda picha ambayo daima ni pepe (virtual), imesimama wima, na imepunguzwa (ndogo kuliko kitu). Picha huundwa nyuma ya kioo, kati ya ncha na sehemu ya focal.

Ushauri kuhusu kioo cha kuendeshea gari:
Kioo kinachofaa kutumika kama kioo cha kuendeshea gari (rear-view mirror) ni kioo mbonyezi (convex mirror). Hii ni kwa sababu kioo mbonyezi huunda picha zilizosimama wima na zilizopunguzwa, na muhimu zaidi, hutoa eneo pana la kuona. Eneo hili pana la kuona humwezesha dereva kuona sehemu kubwa zaidi ya barabara nyuma ya gari, jambo ambalo ni muhimu kwa usalama. Kioo mbonyeo hakifai kwa sababu huunda picha zilizopinduka na zenye eneo dogo la kuona.

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