What is the ranking of the refractive indices of the liquids A, B, and C based on the apparent depth of the coin in each liquid?
The ranking of the refractive indices of the liquids A, B, and C in descending order is:
a. nC, nA, nB
Understanding Refractive Indices Calculation:
Real Depth versus Apparent Depth:
When a coin is placed in a container filled with different liquids, the refractive index of the liquid affects how the coin appears when viewed from above. The real depth of the coin remains constant, but the apparent depth changes due to the refractive index of the liquid.
Calculating the Refractive Index:
1. Liquid A: Apparent Depth = 7 cm
Refractive Index (nA) = Real Depth / Apparent Depth
= d / 7 cm = 0.1428d
2. Liquid B: Apparent Depth = 6 cm
Refractive Index (nB) = Real Depth / Apparent Depth
= d / 6 cm = 0.166d
3. Liquid C: Apparent Depth = 5 cm
Refractive Index (nC) = Real Depth / Apparent Depth
= d / 5 cm = 0.2d
Ranking based on Apparent Depth:
Since the refractive index is inversely proportional to the apparent depth, we can conclude that:
nC > nB > nA
Therefore, the correct ranking of the refractive indices of the liquids A, B, and C in descending order is nC, nA, nB.