What is the apparent position of an object below rectangular block of glass 6cm thick, If a layer of water…

Question

What is the apparent position of an object below rectangular block of glass 6cm thick, If a layer of water 4cm thick is on top of the glass? The refractive indexes of glass and water are 1.5 and 1.33 respectively

ScanSolve AI Tutor · Accepted Answer

Hili ni swali jipya, na nitakutatulia.

Ili kupata nafasi inayoonekana ya kitu kilicho chini ya tabaka mbili za vifaa tofauti, tunajumlisha kina kinachoonekana cha kila tabaka. Kina kinachoonekana ( $d_{apparent}$ ) cha tabaka moja huhesabiwa kwa kutumia kanuni:

d_{apparent} = \frac{d_{real}}{n}

Ambapo $d_{real}$ ni unene halisi wa tabaka na $n$ ni fahirisi ya mtawanyiko wa tabaka hilo.

Tambua unene halisi na fahirisi za mtawanyiko kwa kila tabaka.
- Kwa tabaka la kioo:
  
  Unene halisi wa kioo, $d_g = 6 \text{ cm}$
  
  Fahirisi ya mtawanyiko wa kioo, $n_g = 1.5$
- Kwa tabaka la maji:
  
  Unene halisi wa maji, $d_w = 4 \text{ cm}$
  
  Fahirisi ya mtawanyiko wa maji, $n_w = 1.33$
Kokotoa kina kinachoonekana kinachochangiwa na tabaka la kioo.
$d'_{g} = \frac{d_g}{n_g} = \frac{6 \text{ cm}}{1.5}$ $d'_{g} = 4 \text{ cm}$
Kokotoa kina kinachoonekana kinachochangiwa na tabaka la maji.
$d'_{w} = \frac{d_w}{n_w} = \frac{4 \text{ cm}}{1.33}$ $d'_{w} \approx 3.0075 \text{ cm}$
Jumlisha kina kinachoonekana cha kila tabaka ili kupata nafasi ya jumla inayoonekana ya kitu kutoka juu ya uso wa maji.
$D_{apparent} = d'_{g} + d'_{w}$ $D_{apparent} = 4 \text{ cm} + 3.0075 \text{ cm}$ $D_{apparent} \approx 7.0075 \text{ cm}$
Kuzungusha hadi sehemu mbili za desimali, nafasi inayoonekana ni $7.01 \text{ cm}$ .

Nafasi inayoonekana ya kitu ni $\boxed{7.01 \text{ cm}}$ chini ya uso wa maji.

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What is the apparent position of an object below rectangular block of glass 6cm thick, If a layer of water 4cm thick is on top of the glass? The refractive indexes of glass and water are 1.5 and 1.33 respectively

Answer

Step-by-step solution

Tambua unene halisi na fahirisi za mtawanyiko kwa kila tabaka.

Kokotoa kina kinachoonekana kinachochangiwa na tabaka la kioo.

Kokotoa kina kinachoonekana kinachochangiwa na tabaka la maji.

Jumlisha kina kinachoonekana cha kila tabaka ili kupata nafasi ya jumla inayoonekana ya kitu kutoka juu ya uso wa maji.

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