Answer :
To find the apparent displacement of the stone when water is poured into the bucket to a depth of 20 cm with a refractive index of 1.33, we will follow these steps:
1. Determine the Real Depth:
The real depth of the water is given as 20 cm.
2. Understand the Refractive Index:
The refractive index of water is provided as 1.33. This is a measure of how much light bends when it passes from one medium to another, in this case, from water to air.
3. Calculate the Apparent Depth:
The formula to find the apparent depth when looking vertically into a medium is:
[tex]\[ \text{Apparent Depth} = \frac{\text{Real Depth}}{\text{Refractive Index}} \][/tex]
Plugging in the given values:
[tex]\[ \text{Apparent Depth} = \frac{20 \, \text{cm}}{1.33} \approx 15.0376 \, \text{cm} \][/tex]
4. Calculate the Apparent Displacement:
The apparent displacement is the difference between the real depth and the apparent depth. This is calculated as:
[tex]\[ \text{Apparent Displacement} = \text{Real Depth} - \text{Apparent Depth} \][/tex]
Substituting the values we found:
[tex]\[ \text{Apparent Displacement} = 20 \, \text{cm} - 15.0376 \, \text{cm} \approx 4.9624 \, \text{cm} \][/tex]
Therefore, the apparent displacement of the stone is approximately 4.9624 cm.
1. Determine the Real Depth:
The real depth of the water is given as 20 cm.
2. Understand the Refractive Index:
The refractive index of water is provided as 1.33. This is a measure of how much light bends when it passes from one medium to another, in this case, from water to air.
3. Calculate the Apparent Depth:
The formula to find the apparent depth when looking vertically into a medium is:
[tex]\[ \text{Apparent Depth} = \frac{\text{Real Depth}}{\text{Refractive Index}} \][/tex]
Plugging in the given values:
[tex]\[ \text{Apparent Depth} = \frac{20 \, \text{cm}}{1.33} \approx 15.0376 \, \text{cm} \][/tex]
4. Calculate the Apparent Displacement:
The apparent displacement is the difference between the real depth and the apparent depth. This is calculated as:
[tex]\[ \text{Apparent Displacement} = \text{Real Depth} - \text{Apparent Depth} \][/tex]
Substituting the values we found:
[tex]\[ \text{Apparent Displacement} = 20 \, \text{cm} - 15.0376 \, \text{cm} \approx 4.9624 \, \text{cm} \][/tex]
Therefore, the apparent displacement of the stone is approximately 4.9624 cm.
