The base of a tank is a horizontal glass plate 8 cm thick $(μ = 1.6)$ .above this is a layer of liquid of thickness 4.5 cm $(μ = 1.5)$ and upon this floats a layer of water 12 cm thick $(μ = \frac{4}{3})$ .Looking from the above, the apparent position of the spot on the bottom of the tank is

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17 cm

21 cm

35cm

19 cm

answer is A.

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Detailed Solution

Thickness of glass plate

d_{1} = 8 cm; μ_{1} = 1.6

Thickness of liquid $d_{2} = 4.5 cm; μ_{2} = 1.5$

Thickness of water $d_{3} = 12 cm; μ_{3} = \frac{4}{3}$

Apparent depth $= \frac{d_{1}}{μ_{1}} + \frac{d_{2}}{μ_{2}} + \frac{d_{3}}{μ_{3}}$

$= \frac{8}{1.6} + \frac{4.5}{1.5} + 12 \times \frac{3}{4}$

$= \frac{80}{16} + \frac{45}{15} + 9$

$= 5 + 3 + 9$

$= 17 cm$

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