Lense with two mediums speed of a fish in an aquarium

[goWlfpack]

Homework Statement

A goldfish is swimming at 4.40 cm/s toward the front wall of a rectangular aquarium. What is the apparent speed of the fish as measured by an observer looking in from outside the front wall of the tank? The index of refraction of water is 1.333.

Homework Equations

p = - (n1/n2) q
where q is object distance, p is image distance, and n1 and n2 are the respective indices of refraction mediums

The Attempt at a Solution

i plugged it in using water (1.33) as medium 1 and air (1.00) for n2. I plugged in 4.40 for q. I got 5.85 and that got the red x... help

 

[alphysicist]

Hi goWlfpack,

Homework Statement

A goldfish is swimming at 4.40 cm/s toward the front wall of a rectangular aquarium. What is the apparent speed of the fish as measured by an observer looking in from outside the front wall of the tank? The index of refraction of water is 1.333.

Homework Equations

p = - (n1/n2) q
where q is object distance, p is image distance, and n1 and n2 are the respective indices of refraction mediums

The Attempt at a Solution

i plugged it in using water (1.33) as medium 1 and air (1.00) for n2. I plugged in 4.40 for q. I got 5.85 and that got the red x... help

Here p is the object distance and q is the image distance; you seem to have these switched with each other.

 

[thomate1]

I would suggest double-checking your calculations and making sure that you are using the correct formula for this situation. It seems like you may have used the thin lens equation, which is not applicable in this case. Instead, you should use the Snell's law equation, which relates the angle of incidence and refraction of light at a boundary between two mediums. In this case, the light rays from the fish will be refracted as they pass from water (n1 = 1.333) to air (n2 = 1.00). The equation for Snell's law is n1sinθ1 = n2sinθ2, where θ1 and θ2 are the angles of incidence and refraction, respectively. Since the light rays are passing from a higher index of refraction (water) to a lower one (air), the angle of refraction will be larger than the angle of incidence. From this, you can calculate the apparent speed of the fish as seen from outside the aquarium.