Question

In Tachometry value of additive constant will become zero with the addition of

• A. Objective glass
• B. Analytic lens
• C. Focusing glass
• D. Stadia diaphragm

Hint:

The word "anallactic" means "unchanging" or "invariable".
The lens is so named because it makes the angle subtended by the stadia hairs invariable with respect to the instrument's center, thus eliminating the additive constant.
Most modern tachometers have internal focusing and are designed to be anallactic without a separate lens.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks which component, when added to a tachometer, makes the additive constant zero.

Step 2: Detailed Explanation:
A tachometer is a type of theodolite used for rapid distance and elevation measurement.
The distance (D) from the instrument to a staff is calculated using the formula:
\[ D = kS + C \] where: - \(S\) is the stadia intercept (the difference between the top and bottom stadia hair readings).
- \(k\) is the multiplying constant (usually 100).
- \(C\) is the

additive constant.
The additive constant \(C\) arises because the measurement is referenced from the center of the instrument, but the apex of the measuring angle is at the focal point of the objective lens, which is a small distance away from the center.
An

anallactic lens (sometimes spelled analytic lens) is an additional convex lens fitted between the objective lens and the diaphragm of an external focusing telescope.
The optical properties of this lens are designed to shift the apex of the measuring angle to coincide exactly with the vertical axis of the instrument.
This modification makes the additive constant \(C\) become zero, simplifying the distance calculation to \(D = kS\).

Step 3: Final Answer:
The addition of an analytic lens makes the additive constant zero.
This corresponds to option (B).