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A vertical photograph was taken from an aircraft flying at an altitude of 2000 m above mean sea level. The focal length of the camera is 175 mm. The scale of the photograph for a hill of an elevation of 250 m is
  • a)
    1/10000
  • b)
    1/150000
  • c)
    1/200000
  • d)
    1/25000
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Scale of Photograph

Given:

Altitude of aircraft (h) = 2000 m

Focal length of camera (f) = 175 mm = 0.175 m

Elevation of hill (H) = 250 m

We need to find the scale of the photograph for a hill of an elevation of 250 m.

Let's consider the triangle formed by the aircraft, the hill, and the camera. We can use similar triangles to relate the height of the hill on the photograph (h') to the actual height of the hill (H).

Using the similar triangles, we get:

h'/f = (H + h)/h

h' = f*(H + h)/h

Substituting the given values, we get:

h' = 0.175*(250 + 2000)/2000 = 0.22125 m

The scale of the photograph is given by the ratio of the distance on the photograph to the actual distance. Since the photograph is taken vertically, the scale is the same in both the horizontal and vertical directions. Therefore, we can use the height of the hill on the photograph (h') as the distance on the photograph.

The actual distance corresponding to the height of the hill on the photograph is given by:

d = H*(h'/h) = 250*(0.22125/2000) = 0.02765625 km

The scale of the photograph is the ratio of the distance on the photograph to the actual distance:

scale = (1 cm on photograph)/(d in km) = 1/(d*100000) = 1/0.02765625 = 1/10000

Therefore, the correct option is (A) 1/10000.
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A vertical photograph was taken from an aircraft flying at an altitude of 2000 m above mean sea level. The focal length of the camera is 175 mm. The scale of the photograph for a hill of an elevation of 250 m isa)1/10000b)1/150000c)1/200000d)1/25000Correct answer is option 'A'. Can you explain this answer?
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