Answer :
Final answer:
The speck of dust under the ice cube appears to be closer to the viewer than it actually is due to the refraction of light. Using Snell's law and the given index of refraction for ice, we estimate that the speck of dust appears to be 38.2 cm below the top surface of the ice cube when viewed from directly above.
Explanation:
To determine the location of the image of the speck of dust under the cubical block of ice, we'll rely on the principles of light refraction. Refraction is the bending of light as it passes from one medium to another, and it's quantified by the index of refraction. In this case, we're dealing with light passing from ice to air. The index of refraction (n) of ice is given as 1.309.
When light moves from a medium with a higher refractive index to one with a lower index, its path bends away from the perpendicular. Knowing the height of the ice cube and its index of refraction, we can calculate how much the light gets refracted. As a result, the location of the speck appears closer to the observer than it actually is.
When light refracts, and as per Snell's law, the following relationship exists:
n1/n2 = d2/d1
Where n1 is the index of refraction of the first medium (in this case, ice), n2 is the index of refraction of the second medium (air, which has an index of 1), d1 is the actual depth, and d2 is the depth as it appears. By inputting our values into this formula:
1.309/1 = 50/d2
Then, solving for d2, we estimate that the speck of dust appears to be approximately 38.2 cm below the top surface of the ice cube when viewed from directly above. Therefore, the correct answer is 38.2 cm.
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