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What is the value of additive constant in anallactic lens?
100
An anallactic lens is a specialized convex lens inserted between the diaphragm and the objective lens of a tacheometer to eliminate the additive constant. By optical design, this lens ensures that all lines of sight effectively originate from the center of the instrument's vertical axis, making the additive constant equal to zero.
An anallactic lens is a specialized convex lens inserted between the diaphragm and the objective lens of a tacheometer to eliminate the additive constant. By optical design, this lens ensures that all lines of sight effectively originate from the center of the instrument's vertical axis, making the additive constant equal to zero.
D=K⋅s+C
C=f+d
In a standard telescope, the distance equation is D=K⋅s+C, where K is the multiplying constant (f/i) and C is the additive constant (f+d). By introducing an anallactic lens at a specific position, the light rays are refracted such that the vertex of the visual rays is shifted to the trunnion axis of the telescope, forcing the additive constant C to become zero.
The primary purpose of an anallactic lens is to simplify tacheometric calculations by eliminating the additive constant.
For instruments fitted with an anallactic lens, the distance D is directly proportional to the staff intercept s, i.e., D=100s.
It makes the instrument reach 'zero' constant, which is a significant advantage in field measurements.
Simplifies distance computation by removing the additive constant component.
Reduces manual calculation errors in the field.
Adds complexity and cost to the optical system of the telescope.
Slightly reduces the light-gathering capacity due to additional lens elements.
Stadia Tacheometry
Topographic surveying for rapid distance measurement
The constant K (multiplying constant) typically remains 100 for most modern tacheometers.
Anallactic lenses are most commonly found in internal focusing telescopes.
B is correct — The additive constant in a telescope provided with an anallactic lens is equal to 0.
Always remember that while the additive constant is 0 with an anallactic lens, the multiplying constant K is maintained at 100 to allow for convenient staff intercept measurements.