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A tank Contains a slab of glass 8cm thick and refractive Index 1.16. Above this is a depth of 4.5cm of water and upon this floats 6cm of water of refractive Index of 4/3. To an observer looking down from above, what the apparent position of a mark on the bottom of the tank?

Physics

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Answers

3 parts
1

12.83 cm12.83 \text{ cm}

2

7.01 cm7.01 \text{ cm}

3

2.56 cm2.56 \text{ cm}

Step-by-step solution

9 steps

Nimepata maswali matatu kwenye picha uliyotuma. Nitayatatua yote matatu.


Part 1· 3 steps

Tangi lina kioo chenye unene wa 8 cm8 \text{ cm} na fahirisi ya mtawanyiko 1.5. Juu yake kuna kimiminika chenye kina cha 4.5 cm4.5 \text{ cm} na fahirisi ya mtawanyiko 1.5. Juu ya hicho kimiminika kuna maji yenye kina cha 6 cm6 \text{ cm} na fahirisi ya mtawanyiko 43\frac{4}{3}. Kwa mwangalizi anayetazama chini kutoka juu, kina kinachoonekana cha alama iliyo chini ya tangi ni kipi?

  1. Tambua unene halisi (tt) na fahirisi ya mtawanyiko (nn) kwa kila safu.

    • Safu ya kioo: tg=8 cmt_g = 8 \text{ cm}, ng=1.5n_g = 1.5
    • Safu ya kimiminika: tl=4.5 cmt_l = 4.5 \text{ cm}, nl=1.5n_l = 1.5
    • Safu ya maji: tw=6 cmt_w = 6 \text{ cm}, nw=43n_w = \frac{4}{3}
  2. Tumia kanuni ya kina kinachoonekana (dapp=tnd_{app} = \frac{t}{n}) kwa kila safu.

    Kina kinachoonekana jumla (dtotal_appd_{total\_app}) ni jumla ya kina kinachoonekana cha kila safu:

    dtotal_app=tgng+tlnl+twnwd_{total\_app} = \frac{t_g}{n_g} + \frac{t_l}{n_l} + \frac{t_w}{n_w}
  3. Badilisha thamani na ufanye hesabu.

    dtotal_app=8 cm1.5+4.5 cm1.5+6 cm4/3d_{total\_app} = \frac{8 \text{ cm}}{1.5} + \frac{4.5 \text{ cm}}{1.5} + \frac{6 \text{ cm}}{4/3} dtotal_app=83/2 cm+3 cm+(6×34) cmd_{total\_app} = \frac{8}{3/2} \text{ cm} + 3 \text{ cm} + \left(6 \times \frac{3}{4}\right) \text{ cm} dtotal_app=163 cm+3 cm+184 cmd_{total\_app} = \frac{16}{3} \text{ cm} + 3 \text{ cm} + \frac{18}{4} \text{ cm} dtotal_app=5.333... cm+3 cm+4.5 cmd_{total\_app} = 5.333... \text{ cm} + 3 \text{ cm} + 4.5 \text{ cm} dtotal_app=12.833... cmd_{total\_app} = 12.833... \text{ cm}

    Kina kinachoonekana cha alama ni 12.83 cm\boxed{12.83 \text{ cm}}.


Part 2

7.01 cm7.01 \text{ cm}

Kina kinachoonekana cha kitu kilicho chini ya kizuizi cha kioo chenye umbo la mstatili chenye unene wa 6 cm6 \text{ cm} ni kipi? Ikiwa safu ya maji yenye unene wa 4 cm4 \text{ cm} iko juu ya kioo? Fahirisi za mtawanyiko za kioo na maji ni 1.5 na 1.33 mtawalia.

  1. Tambua unene halisi (tt) na fahirisi ya mtawanyiko (nn) kwa kila safu.

    • Safu ya maji (juu): tw=4 cmt_w = 4 \text{ cm}, nw=1.33n_w = 1.33
    • Safu ya kioo (chini): tg=6 cmt_g = 6 \text{ cm}, ng=1.5n_g = 1.5
  2. Tumia kanuni ya kina kinachoonekana (dapp=tnd_{app} = \frac{t}{n}) kwa kila safu.

    Kina kinachoonekana jumla (dtotal_appd_{total\_app}) ni jumla ya kina kinachoonekana cha kila safu:

    dtotal_app=twnw+tgngd_{total\_app} = \frac{t_w}{n_w} + \frac{t_g}{n_g}
  3. Badilisha thamani na ufanye hesabu.

    dtotal_app=4 cm1.33+6 cm1.5d_{total\_app} = \frac{4 \text{ cm}}{1.33} + \frac{6 \text{ cm}}{1.5} dtotal_app≈3.0075 cm+4 cmd_{total\_app} \approx 3.0075 \text{ cm} + 4 \text{ cm} dtotal_app≈7.0075 cmd_{total\_app} \approx 7.0075 \text{ cm}

    Kina kinachoonekana cha kitu ni 7.01 cm\boxed{7.01 \text{ cm}}.


Part 3

2.56 cm2.56 \text{ cm}

Slabu tatu za aina tofauti za vioo zimewekwa juu ya nyingine kwa mpangilio ufuatao kutoka chini:

Fahirisi ya Mtawanyiko (nn)Unene (tt) (cm)
1.41.2
1.51.8
1.60.8
Alama iliyo kwenye meza ya juu itaonekana wapi?

Kumbuka: Nimefasiri "alama iliyo kwenye meza ya juu" kama alama iliyo chini ya slabu zote, kwenye meza ambayo slabu zimewekwa.

  1. Tambua unene halisi (tt) na fahirisi ya mtawanyiko (nn) kwa kila slabu.

    • Slabu ya 1 (chini): t1=1.2 cmt_1 = 1.2 \text{ cm}, n1=1.4n_1 = 1.4
    • Slabu ya 2 (kati): t2=1.8 cmt_2 = 1.8 \text{ cm}, n2=1.5n_2 = 1.5
    • Slabu ya 3 (juu): t3=0.8 cmt_3 = 0.8 \text{ cm}, n3=1.6n_3 = 1.6
  2. Tumia kanuni ya kina kinachoonekana (dapp=tnd_{app} = \frac{t}{n}) kwa kila slabu.

    Kina kinachoonekana jumla (dtotal_appd_{total\_app}) ni jumla ya kina kinachoonekana cha kila slabu:

    dtotal_app=t1n1+t2n2+t3n3d_{total\_app} = \frac{t_1}{n_1} + \frac{t_2}{n_2} + \frac{t_3}{n_3}
  3. Badilisha thamani na ufanye hesabu.

    dtotal_app=1.2 cm1.4+1.8 cm1.5+0.8 cm1.6d_{total\_app} = \frac{1.2 \text{ cm}}{1.4} + \frac{1.8 \text{ cm}}{1.5} + \frac{0.8 \text{ cm}}{1.6} dtotal_app≈0.8571 cm+1.2 cm+0.5 cmd_{total\_app} \approx 0.8571 \text{ cm} + 1.2 \text{ cm} + 0.5 \text{ cm} dtotal_app≈2.5571 cmd_{total\_app} \approx 2.5571 \text{ cm}

    Alama iliyo kwenye meza itaonekana kuwa kwenye kina cha 2.56 cm\boxed{2.56 \text{ cm}}.

    3 zimekamilika, zimebaki 2 leo. Unapiga hatua.

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