Final answer:
The image of the speck of dust when viewed from directly above through the cubical block of ice appears to be 37.44 cm below the upper surface of the ice, calculated using the index of refraction of ice which is 1.309.
Step-by-step explanation:
To locate the image of the speck of dust when viewed from directly above through the cubical block of ice, we use Snell's law and the concept of refraction. When light enters a material with a different index of refraction, its path bends. In the case of this ice block with an index of refraction of 1.309, light rays bend when entering and exiting the block. The depth at which the speck appears can be found using the formula:
d' = d / n
where:
- d' is the apparent depth,
- d is the actual depth, and
- n is the index of refraction of the material (ice in this case).
The actual depth of the speck is equal to the edge length of the block, since it's placed on the level floor. Substituting these values in the formula we get,
d' = 49.0 cm / 1.309 ≈ 37.44 cm
Therefore, the speck of dust will appear to be 37.44 cm below the upper surface of the ice when viewed from directly above.