Question

Write principle of stadia method.

Answer 1

Principle of stadia method: The stadia method is based on the principle that the ratio of the perpendicular to the base is constant in similar isosceles triangles.

In figure, let two rays OA and OB be equally inclined to central ray OC.

Let A2B2, A1B1 and AB be the staff intercepts. Evidently, 

This constant k entirely depends upon the magnitude of the angle β.

OR

In actual practice, observations may be made with either horizontal line of sight or with inclined line of sight. In the later case the staff may be kept either vertically or normal to the line of sight. 

Consider the figure, in which O is the optical centre of the objective of an external focusing

telescope.

Let A, C, and B = the points cut by the three lines of sight corresponding to three wires.

 b, c, and a = top, axial and bottom hairs of the diaphragm.

 ab = i = interval b/w the stadia hairs (stadia interval)

 AB = s = staff intercept;

 f = focal length of the objective

 f1 = horizontal distance of the staff from the optical centre of the objective

 f2 = horizontal distance of the cross-wires from O.

 d = distance of the vertical axis of the instrument from O.

 D = horizontal distance of the staff from the vertical axis of the instruments.

 M = centre of the instrument, corresponding to the vertical axis.

Since the rays BOb and AOa pass through the optical centre, they are straight so that AOB and aOb are similar. Hence, f1/f2 = s/i

Again, since f1 and f2 are conjugate focal distances, we have from lens formula

 1/f = 1/f2 + 1/f1

 i.e.f1/f – 1 = f1/f2 =s/i

 or f1 = f/i s + f

Horizontal distance between the axis and the staff is D = f1 + d

 D = (f/i)s + (f+d)

Above equation is known as the distance equation. In order to get the horizontal distance, therefore, the staff intercept s is to be found by subtracting the staff readings corresponding to the top and bottom stadia hairs. The constant f/i is known as the multiplying constant or stadia interval factor and the constant (f + d) is known as the additive constant of the instrument