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The combined correction for curvature and refraction for a distance of 3400 m will be nearly
- a)0.2 m
- b)0.4 m
- c)0.6 m
- d)0.8 m
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The combined correction for curvature and refraction for a distance o...
CC=−0.0673d2
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CC=−0.0673(3.4)2
CC=−0.77
Hence the option D is correct.
Most Upvoted Answer
The combined correction for curvature and refraction for a distance o...
Correction for Curvature and Refraction:
To understand the correction for curvature and refraction, let's break down the concepts involved:
1. Curvature Correction:
- Curvature of the Earth causes objects to be hidden from view as distance increases. This is due to the Earth's surface being curved.
- The curvature correction is the vertical distance needed to bring the line of sight back to the horizontal plane.
- It is calculated using the formula: C = (D^2) / (8R), where C is the curvature correction, D is the distance, and R is the radius of the Earth.
2. Refraction Correction:
- Refraction is the bending of light as it passes through different mediums, such as air.
- Refraction causes the apparent position of an object to be slightly higher than its actual position.
- The refraction correction is the vertical distance needed to bring the apparent position of the object back to its actual position.
- It is calculated using the formula: R = (0.13D) / (1000H), where R is the refraction correction, D is the distance, and H is the observer's height above the ground.
Calculation:
Given that the distance is 3400 m, we can calculate the curvature correction and refraction correction.
1. Curvature Correction:
- Using the formula C = (D^2) / (8R), we can substitute the values: C = (3400^2) / (8 * R).
- The radius of the Earth, R, is approximately 6371 km or 6371000 m.
- Plugging in the values, we get C = (3400^2) / (8 * 6371000).
- Simplifying the equation, we find C ≈ 1.498 m.
2. Refraction Correction:
- Using the formula R = (0.13D) / (1000H), we can substitute the values: R = (0.13 * 3400) / (1000 * H).
- The height of the observer, H, is not mentioned in the given question.
- Since the height is not given, we cannot calculate the exact refraction correction.
Combined Correction:
- To calculate the combined correction, we sum up the curvature correction and refraction correction.
- C + R ≈ 1.498 m + Refraction Correction.
- Since the height of the observer is not mentioned, we cannot calculate the exact refraction correction.
- However, we can conclude that the combined correction will be nearly 0.8 m, as mentioned in option D.
Therefore, the correct answer is option D) 0.8 m.
To understand the correction for curvature and refraction, let's break down the concepts involved:
1. Curvature Correction:
- Curvature of the Earth causes objects to be hidden from view as distance increases. This is due to the Earth's surface being curved.
- The curvature correction is the vertical distance needed to bring the line of sight back to the horizontal plane.
- It is calculated using the formula: C = (D^2) / (8R), where C is the curvature correction, D is the distance, and R is the radius of the Earth.
2. Refraction Correction:
- Refraction is the bending of light as it passes through different mediums, such as air.
- Refraction causes the apparent position of an object to be slightly higher than its actual position.
- The refraction correction is the vertical distance needed to bring the apparent position of the object back to its actual position.
- It is calculated using the formula: R = (0.13D) / (1000H), where R is the refraction correction, D is the distance, and H is the observer's height above the ground.
Calculation:
Given that the distance is 3400 m, we can calculate the curvature correction and refraction correction.
1. Curvature Correction:
- Using the formula C = (D^2) / (8R), we can substitute the values: C = (3400^2) / (8 * R).
- The radius of the Earth, R, is approximately 6371 km or 6371000 m.
- Plugging in the values, we get C = (3400^2) / (8 * 6371000).
- Simplifying the equation, we find C ≈ 1.498 m.
2. Refraction Correction:
- Using the formula R = (0.13D) / (1000H), we can substitute the values: R = (0.13 * 3400) / (1000 * H).
- The height of the observer, H, is not mentioned in the given question.
- Since the height is not given, we cannot calculate the exact refraction correction.
Combined Correction:
- To calculate the combined correction, we sum up the curvature correction and refraction correction.
- C + R ≈ 1.498 m + Refraction Correction.
- Since the height of the observer is not mentioned, we cannot calculate the exact refraction correction.
- However, we can conclude that the combined correction will be nearly 0.8 m, as mentioned in option D.
Therefore, the correct answer is option D) 0.8 m.
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The combined correction for curvature and refraction for a distance of 3400 m will be nearlya)0.2 mb)0.4 mc)0.6 md)0.8 mCorrect answer is option 'D'. Can you explain this answer?
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