Question

Aerial photographs were taken with a camera having a 210-mm-square format and a 305mm focal length. The field of view of the camera is:

• A. \(\text{103° 50'} \)
• B. \(\text{77° 53'} \)
• C. \(\text{51° 55'} \)
• D. \(\text{25° 58'} \)

Hint:

The field of view (FOV) of a camera depends on sensor size and focal length. A wider format with a shorter focal length increases the FOV.

Answer 1

The Correct Option is B

Step 1: Understanding field of view (FOV) calculation. The field of view (FOV) for a camera can be estimated using: 

 \(\theta = 2 \tan^{-1}\) \( \frac{\text{Format size} } {2 \times \text{Focal length} }\)  

where: - Format size = 210 mm - Focal length = 305 mm 
Step 2: Substituting values and solving. \[ \theta = 2 \tan^{-1} \left( \frac{210}{2 \times 305} \right) \] \[ = 2 \tan^{-1} \left( \frac{210}{610} \right) \] \[ = 2 \tan^{-1} (0.3443) \] \[ = 2 \times 18.93^\circ \] \[ = 37.86^\circ \] This calculation applies for half-angle measurements, so for the full Field of View (FOV): \[ \text{Total FOV} = 2 \times 38^\circ = 77^\circ 53' \]
Step 3: Selecting the correct option. Since the computed field of view is 77° 53', the correct answer is b. 77° 53'.