Following are the data of an externally focusing telescope used for a tacheometric survey. Staff intercept: 1.52 m Interval between stadia hair: 5 mm Distance between the vertical axis of the telescope and the objective: 120 mm Focal length of the objective: 300 mm The value of the multiplying constant is:
- A12.67
- B2.5
- C60Correct
- D24
Solution
Concept
For an external focusing telescope, the multiplying constant k = f/i, where f is the focal length of the objective and i is the stadia hair interval.
Formula
k = f/i ; C = f + d ; D = k×s + C
Step-by-step solution
1. Focal length f = 300 mm, stadia interval i = 5 mm. 2. Multiplying constant k = f/i = 300/5 = 60. 3. (Extra) Additive constant C = f + d = 300 + 120 = 420 mm = 0.42 m. 4. (Extra) Distance D = 60 × 1.52 + 0.42 = 91.62 m.
Explanation
The multiplying constant depends only on the focal length and the stadia hair interval. Here it is 300/5 = 60. The staff intercept and the distance d are not needed for k.
Why the other options are wrong
A: 12.67 does not come from f/i. B: 2.5 is f/d (300/120), which is wrong. D: 24 is d/i (120/5), which is wrong.
Shortcut
k = f/i directly. Ignore the extra data.
Common mistake
Using the staff intercept or d to find k. These are used for the additive constant and the distance only.
Correct answer: C) 60