Final answer:
The question deals with the refraction of light as it passes from water to air and how it affects the perceived height of an object. The actual height of the diving board is related to the apparent height and the index of refraction; however, without specific values or angles, a numerical answer cannot be provided.
Step-by-step explanation:
The subject of the question is Physics, and the problem pertains to the concept of refraction and its application in determining the actual height of an object above the surface of the water when viewed from below the surface.
Refraction occurs when light passes from one medium into another, changing speed and bending at the interface. In this scenario, light refracted at the water's surface creates an image of the diving board overhead. The image appears at a different height due to refraction than it would if the water were not there.
The actual height of the diving board above the water can be determined using Snell's Law, which relates the angle of incidence to the angle of refraction and the indices of refraction of the two media. However, since the problem does not provide specific angles or indices of refraction, and instead asks to infer the height of the diving board above the surface from the perceived height, one might apply the principle behind the apparent depth formula, which can be given as:
real depth = apparent depth / (index of refraction of water)
Since the index of refraction of water is typically around 1.33, the real height of the diving board above the swimmer can be found by multiplying the apparent height, 5.75 m, by the index of refraction. However, this does not account for the distance below the surface that the swimmer is viewing from (0.70 m). To calculate the actual height of the diving board above the surface, you would nominally subtract this distance from the product of the apparent height and the index of refraction, but again, without specific values, precise numerical answers cannot be provided.
To fully solve this problem, more data is needed, specifically the angle of incidence and/or the index of refraction for the media involved (air and water).