QuestionJune 14, 2025

A fish looking straight upward spots a berry on a tree branch above the surface of a pond. The fish is at rest 15 cm below the surface.while the berry is positioned 1.5 m above the surface. The index of refraction of water is 1.33. How far away does the berry appear to be from the fish's perspective? Multiple Choice 165 m 15 m 215 m 20m

A fish looking straight upward spots a berry on a tree branch above the surface of a pond. The fish is at rest 15 cm below the surface.while the berry is positioned 1.5 m above the surface. The index of refraction of water is 1.33. How far away does the berry appear to be from the fish's perspective? Multiple Choice 165 m 15 m 215 m 20m
A fish looking straight upward spots a berry on a tree branch above the surface of a pond. The fish is at rest 15 cm below the surface.while the berry is positioned 1.5 m above the surface. The index of refraction of water is 1.33. How far away does the berry appear to be from the fish's perspective? Multiple Choice 165 m 15 m 215 m 20m

Solution
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Answer

1.39 m Explanation 1. Identify the Apparent Depth Formula Use the formula for apparent depth: **d' = \frac{d}{n}**, where d is the real depth and n is the index of refraction. 2. Calculate Real Distance from Fish to Berry The real distance from the fish to the berry is 15 \text{ cm} + 150 \text{ cm} = 165 \text{ cm}. 3. Convert Real Distance to Meters Convert 165 cm to meters: 165 \text{ cm} = 1.65 \text{ m}. 4. Calculate Apparent Distance Apply the formula: d' = \frac{1.65}{1.33} \approx 1.24 \text{ m}. 5. Convert Apparent Distance to Centimeters Convert 1.24 m to centimeters: 1.24 \text{ m} = 124 \text{ cm}. 6. Calculate Total Apparent Distance Add the 15 cm depth of the fish: 124 \text{ cm} + 15 \text{ cm} = 139 \text{ cm}. 7. Convert Total Apparent Distance to Meters Convert 139 cm to meters: 139 \text{ cm} = 1.39 \text{ m}.

Explanation

1. Identify the Apparent Depth Formula<br /> Use the formula for apparent depth: **$d' = \frac{d}{n}$**, where $d$ is the real depth and $n$ is the index of refraction.<br /><br />2. Calculate Real Distance from Fish to Berry<br /> The real distance from the fish to the berry is $15 \text{ cm} + 150 \text{ cm} = 165 \text{ cm}$.<br /><br />3. Convert Real Distance to Meters<br /> Convert 165 cm to meters: $165 \text{ cm} = 1.65 \text{ m}$.<br /><br />4. Calculate Apparent Distance<br /> Apply the formula: $d' = \frac{1.65}{1.33} \approx 1.24 \text{ m}$.<br /><br />5. Convert Apparent Distance to Centimeters<br /> Convert 1.24 m to centimeters: $1.24 \text{ m} = 124 \text{ cm}$.<br /><br />6. Calculate Total Apparent Distance<br /> Add the 15 cm depth of the fish: $124 \text{ cm} + 15 \text{ cm} = 139 \text{ cm}$.<br /><br />7. Convert Total Apparent Distance to Meters<br /> Convert 139 cm to meters: $139 \text{ cm} = 1.39 \text{ m}$.
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