Final answer:
The formula for the apparent depth of a fish in a fish tank using Snell's law is Apparent Depth = n1/n2 · Real Depth, derived from Snell's law and the geometry of the situation.
Step-by-step explanation:
To derive the formula for the apparent depth of a fish in a fish tank using Snell's law, recall that Snell's law is nₑ sin θ1 = nₒ sin θ2, where nₑ is the refractive index of the first medium (usually air), and nₒ is the refractive index of the second medium (water in the fish tank). The angles θ1 and θ2 are the angles of incidence and refraction, respectively.
Assuming that the viewing angle is normal (i.e., the observer is directly above the object), we can simplify this equation by using tan ΰ in place of sin ΰ due to the small refraction angle involved. Using the geometry of the situation, we can form a ratio of the apparent depth to the real depth using the indices of refraction.
The correct formula for the apparent depth is Apparent Depth = nₑ/nₒ · Real Depth, reflecting the ratio of the indices of refraction of the two media involved (air to water).