The scale of a tilted photograph of focal length f, taken from an altitude H, along the plate parallel through plumb point, is A. $$\frac{{\text{f}}}{{{\text{H}}\sec \theta }}$$ B. $$\frac{{{\text{f}}\sec \theta }}{{\text{H}}}$$ C. $$\frac{{\text{f}}}{{\text{H}}}$$ D. $$\frac{{\text{f}}}{{{\text{H}}\cos \frac{1}{2}\theta }}$$

The correct answer is $\frac{{\text{f}}}{{{\text{H}}\sec \theta }}$.

The scale of a tilted photograph is the ratio of the distance between two objects on the photograph to the actual distance between the objects. The focal length of a camera is the distance between the lens and the image sensor when the camera is focused on infinity. The altitude of a camera is the height of the camera above the ground. The plumb point is the point on the ground directly below the camera.

The scale of a tilted photograph can be calculated using the following equation:

$$\text{Scale} = \frac{{\text{f}}}{{{\text{H}}\sec \theta }}}$$

where:

• $\text{f}$ is the focal length of the camera,
• $\text{H}$ is the altitude of the camera, and
• $\theta$ is the angle between the camera’s optical axis and the horizontal.

The scale of a tilted photograph is greater when the focal length of the camera is greater, when the altitude of the camera is greater, and when the angle between the camera’s optical axis and the horizontal is greater.

Option A is incorrect because it does not include the factor of $\sec \theta$. Option B is incorrect because it does not include the factor of $\text{H}$. Option C is incorrect because it does not include the factor of $\sec \theta$. Option D is incorrect because it does not include the factor of $\text{H}$.