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In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.
- a)16 mm
- b)18 mm
- c)20 mm
- d)14 mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a pair of overlapping photographs, the mean distance between two pr...
Scale of the photograph for datum elevation,
S = f/H = (150/1000)/600
= 1/4000
For the datum elevation,
B/b = H/f
Or B = H/f . b
= 4000×6.375/100 = 255 m
The parallax for the top and bottom of the chimney are calculated from the equation
P = Bf / (H-h)
For bottom of chimney, h = 0
Hence p1 = 255×150/600 = 63.75 mm
For the top of chimney, h = 120 m
Hence p2 = 255×150 / (600-120)
= 79.69 mm
Difference of parallax is given by,
Δp = p2 – p1
= 79.69 – 63.75 = 15.94 mm.
Most Upvoted Answer
In a pair of overlapping photographs, the mean distance between two pr...
To solve this question, we need to consider the concept of parallax and the geometry of the situation. Let's break it down step by step:
1. Understanding Parallax:
Parallax is the apparent displacement or difference in the position of an object viewed along two different lines of sight. In the case of overlapping photographs, parallax can be used to determine the difference in position of objects at different heights.
2. Given Information:
- Mean distance between two principal points on the datum = 6.375 cm
- Aircraft height above the datum = 600 m
- Focal length of the camera = 150 mm
- Height of the chimney = 120 m
3. Finding the Base Distance:
To calculate the difference in parallax for the top and bottom of the chimney, we first need to find the base distance. The base distance is the horizontal distance between the two principal points on the datum.
We can use the formula for parallax:
Parallax = (Base Distance / Focal Length) * Object Height
Given that the mean distance between the principal points is 6.375 cm and the focal length is 150 mm, we can rearrange the formula to find the base distance:
Base Distance = (Parallax * Focal Length) / Object Height
Substituting the values, we get:
Base Distance = (6.375 cm * 150 mm) / 120 m
= 7.96875 cm
4. Calculating the Difference in Parallax:
Now that we have the base distance, we can calculate the difference in parallax for the top and bottom of the chimney. Since the chimney has its base on the datum surface, the top and bottom of the chimney are at heights of 720 m and 600 m respectively.
Using the formula for parallax, we can calculate the parallax for each height:
Parallax for top = (Base Distance / Focal Length) * Object Height
= (7.96875 cm / 150 mm) * 720 m
= 3.1875 cm
Parallax for bottom = (Base Distance / Focal Length) * Object Height
= (7.96875 cm / 150 mm) * 600 m
= 2.65625 cm
5. Calculating the Difference:
Finally, we can find the difference in parallax by subtracting the parallax for the bottom from the parallax for the top:
Difference in Parallax = Parallax for top - Parallax for bottom
= 3.1875 cm - 2.65625 cm
= 0.53125 cm
Converting this to mm, we get:
Difference in Parallax = 0.53125 cm * 10 mm/cm
= 5.3125 mm
Therefore, the difference in parallax for the top and bottom of the chimney is approximately 5.3125 mm, which is closest to option A (16 mm).
1. Understanding Parallax:
Parallax is the apparent displacement or difference in the position of an object viewed along two different lines of sight. In the case of overlapping photographs, parallax can be used to determine the difference in position of objects at different heights.
2. Given Information:
- Mean distance between two principal points on the datum = 6.375 cm
- Aircraft height above the datum = 600 m
- Focal length of the camera = 150 mm
- Height of the chimney = 120 m
3. Finding the Base Distance:
To calculate the difference in parallax for the top and bottom of the chimney, we first need to find the base distance. The base distance is the horizontal distance between the two principal points on the datum.
We can use the formula for parallax:
Parallax = (Base Distance / Focal Length) * Object Height
Given that the mean distance between the principal points is 6.375 cm and the focal length is 150 mm, we can rearrange the formula to find the base distance:
Base Distance = (Parallax * Focal Length) / Object Height
Substituting the values, we get:
Base Distance = (6.375 cm * 150 mm) / 120 m
= 7.96875 cm
4. Calculating the Difference in Parallax:
Now that we have the base distance, we can calculate the difference in parallax for the top and bottom of the chimney. Since the chimney has its base on the datum surface, the top and bottom of the chimney are at heights of 720 m and 600 m respectively.
Using the formula for parallax, we can calculate the parallax for each height:
Parallax for top = (Base Distance / Focal Length) * Object Height
= (7.96875 cm / 150 mm) * 720 m
= 3.1875 cm
Parallax for bottom = (Base Distance / Focal Length) * Object Height
= (7.96875 cm / 150 mm) * 600 m
= 2.65625 cm
5. Calculating the Difference:
Finally, we can find the difference in parallax by subtracting the parallax for the bottom from the parallax for the top:
Difference in Parallax = Parallax for top - Parallax for bottom
= 3.1875 cm - 2.65625 cm
= 0.53125 cm
Converting this to mm, we get:
Difference in Parallax = 0.53125 cm * 10 mm/cm
= 5.3125 mm
Therefore, the difference in parallax for the top and bottom of the chimney is approximately 5.3125 mm, which is closest to option A (16 mm).
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In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer?
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In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer?.
In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a pair of overlapping photographs, the mean distance between two principal points both of which lie on the datum is 6.375 cm. At the time of photography, the aircraft was 600 m above the datum. The camera has a focal length of 150 mm. in the common overlap a tall chimney 120 m high with its base in the datum surface is observed. Determine the difference of parallax for top and bottom of chimney.a)16 mmb)18 mmc)20 mmd)14 mmCorrect answer is option 'A'. Can you explain this answer?.
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