Final answer:
To locate the apparent position of a goldfish inside a spherical fishbowl, Snell's Law is applied. Considering the refraction of water with an index of 1.33, the fish 3.0 cm from the wall appears to be approximately 2.26 cm from the wall to an outside observer.
Step-by-step explanation:
The question is asking where a goldfish appears to be located when viewed from outside a spherical fishbowl filled with water, taking into account the refraction of light. The phenomenon of light bending due to a change in speed when moving from one medium to another, such as water to air, is known as refraction. To find the apparent position of the goldfish, Snell's Law must be used, which relates the angle of incidence to the angle of refraction and the indices of refraction of the two media.
Using the given index of refraction of water (1.33) and assuming air has an index of refraction of approximately 1, along with the geometry of the situation (a fish 3.0 cm from the wall inside a spherical bowl of 8.0 cm radius), we can compute the apparent depth using the formula for apparent depth, which is given by the real depth divided by the index of refraction. In this case, the apparent depth is 3.0 cm / 1.33, which results in approximately 2.26 cm. Therefore, the fish appears to be 2.26 cm from the wall of the bowl to an observer outside.