Answer: 0.75 ft
Explanation:
This situation is due to Refraction, a phenomenon in which a wave (the light in this case) bends or changes its direction when passing through a medium with an index of refraction different from the other medium. In this context, the index of refraction is a number that describes how fast light propagates through a medium or material.
In addition, we have the following equation that states a relationship between the apparent depth [tex]{d}^{*}[/tex] and the actual depth [tex]d[/tex]:
[tex]{d}^{*}=d\frac{{n}_{1}}{{n}_{2}}[/tex] (1)
Where:
[tex]n_{1}=1[/tex] is the air's index of refraction
[tex]n_{2}=\frac{4}{3}=1.33[/tex] water's index of refraction.
[tex]d=1 ft[/tex] is the actual depth of the quarters
Now. when [tex]n_{1}[/tex] is smaller than [tex]n_{2}[/tex] the apparent depth is smaller than the actual depth. And, when [tex]n_{1}[/tex] is greater than [tex]n_{2}[/tex] the apparent depth is greater than the actual depth.
Let's prove it:
[tex]{d}^{*}=1 ft\frac{1}{1.33}[/tex] (2)
Finally we find the aparent depth of the quarters, which is smaller than the actual depth:
[tex]{d}^{*}=0.75 ft[/tex]
