The scale of a tilted photograph of focal length f taken from an altitude H, along the plate parallel through principal 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 $\boxed{\frac{{\text{f}}}{{{\text{H}}\sec \theta }}}$.

The scale of a photograph is the ratio of the distance between two objects on the photograph to the distance between the same two objects on the ground. In the case of a tilted photograph, the scale is not constant, but varies depending on the angle of the camera to the ground.

The formula for the scale of a tilted photograph is:

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

where:

• $f$ is the focal length of the camera
• $H$ is the altitude of the camera
• $\theta$ is the angle of the camera to the ground

The scale is greatest when the camera is perpendicular to the ground, and decreases as the camera is tilted. This is because the distance between two objects on the photograph is greater when the camera is tilted, so the scale must be smaller to compensate.

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 $f$. Option C is incorrect because it does not include the factor of $\theta$. Option D is incorrect because it does not include the factor of $f$ or $\theta$.