a photograph with a tilt of 3 degrees was taken with a camera of focal length f 150 mm. An image q lies on the part of the photograph upward of the axis of tilt such that the radial distance from the principal point p to q is 65 mm. If the angle between line pq is 15 degrees compute the ilt dispacement of q
Question
a photograph with a tilt of 3 degrees was taken with a camera of focal length f 150 mm. An image q lies on the part of the photograph upward of the axis of tilt such that the radial distance from the principal point p to q is 65 mm. If the angle between line pq is 15 degrees compute the ilt dispacement of q
Solution
To compute the tilt displacement of point q, we can use the following steps:
Step 1: Convert the tilt angle from degrees to radians.
- Tilt angle (θ) = 3 degrees
- Tilt angle in radians (θ_rad) = θ * π / 180
Step 2: Calculate the tilt displacement of point q.
- Tilt displacement (d) = f * tan(θ_rad)
Step 3: Calculate the horizontal displacement of point q.
- Horizontal displacement (h) = d * cos(15 degrees)
Step 4: Calculate the vertical displacement of point q.
- Vertical displacement (v) = d * sin(15 degrees)
Step 5: Calculate the tilt displacement of point q.
- Tilt displacement of q = √(h^2 + v^2)
Now, let's substitute the given values into the equations:
Step 1: Convert the tilt angle from degrees to radians.
- θ_rad = 3 * π / 180 ≈ 0.0524 radians
Step 2: Calculate the tilt displacement of point q.
- d = 150 mm * tan(0.0524 radians) ≈ 8.74 mm
Step 3: Calculate the horizontal displacement of point q.
- h = 8.74 mm * cos(15 degrees) ≈ 8.49 mm
Step 4: Calculate the vertical displacement of point q.
- v = 8.74 mm * sin(15 degrees) ≈ 2.39 mm
Step 5: Calculate the tilt displacement of point q.
- Tilt displacement of q = √(8.49 mm^2 + 2.39 mm^2) ≈ 8.82 mm
Therefore, the tilt displacement of point q is approximately 8.82 mm.
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