Final answer:
The actual depth of the fish in the bowl is calculated using Snell's law and the given indices of refraction for water and air, resulting in the fish being 7.98 cm away from the wall of the bowl.
Step-by-step explanation:
The question involves calculating the actual depth of a fish swimming in a fishbowl, given the apparent depth as observed by an onlooker. To find the actual depth, we must use Snell's law to account for the refraction of light as it passes from water to air. The index of refraction of water (1.33) and the index of refraction of air (1.00) are given, along with the apparent depth (6.0 cm).
Snell's law states that n1sin(θ1) = n2sin(θ2), where n represents the index of refraction and θ represents the angle of incidence and refraction. The actual depth dactual is related to the apparent depth dapparent by the formula:
dactual = dapparent (nwater / nair)
Substituting the given values, we have:
dactual = 6.0 cm (1.33 / 1.00) = 7.98 cm
Therefore, the fish is actually swimming 7.98 cm away from the wall of the bowl.