Explain basic principle of Stadia Method.

Let us consider the external focusing type of telescope and let us consider the line of sight to be horizontal. Let,

`f=`focal length of the object glass.

`i=`stadia hair interval `=ab`

 `S=`Staff intercept

  `=AB`

`c=`siatance from O to the vertical axis of the instrument

`d=`distance from O to the staff

`d'=`distance from O to the plane of the diaphragm

`D=`horizontal axis from the vertical axis to the staff.

Now, from triangle AOB and aOb, we have,

`d/d'=u/v=S/i`.......(i)

Again, from lens formula, we have,

`1/f=1/u+1/v`

Multiplying both sides by `uf`, we get,

`(uf)/f=(uf)/u+(uf)/v`

or, `u=(uf)/v+f`....(ii)

Now, from (i) and (ii), we get,

`u=f+f/(i/S)`

 `=f+(fS)/i`

Adding a constant `c` on both sides, we get,

`u+c=(fS)/i+(f+c)`

Again from figure,

`D=u+c`

Thus,`D=(fS)/i=(f+c)

Also, let `K=f/i` and `C=f+c`,

then the abo....

Let us consider the external focusing type of telescope and let us consider the line of sight to be horizontal. Let,

`f=`focal length of the object glass.

`i=`stadia hair interval `=ab`

 `S=`Staff intercept

  `=AB`

`c=`siatance from O to the vertical axis of the instrument

`d=`distance from O to the staff

`d'=`distance from O to the plane of the diaphragm

`D=`horizontal axis from the vertical axis to the staff.

Now, from triangle AOB and aOb, we have,

`d/d'=u/v=S/i`.......(i)

Again, from lens formula, we have,

`1/f=1/u+1/v`

Multiplying both sides by `uf`, we get,

`(uf)/f=(uf)/u+(uf)/v`

or, `u=(uf)/v+f`....(ii)

Now, from (i) and (ii), we get,

`u=f+f/(i/S)`

 `=f+(fS)/i`

Adding a constant `c` on both sides, we get,

`u+c=(fS)/i+(f+c)`

Again from figure,

`D=u+c`

Thus,`D=(fS)/i=(f+c)

Also, let `K=f/i` and `C=f+c`,

then the above expression becomes,

`D=K*S+C`.....(iii)

This is the standard equation used to explain the principle of stadia hair system.

Where `K` is the multiplying constant and `C` is the additive constant.

Now, 

for analytic lens, `K=100` and `C=0`

for external focusing telescope, `C=0.3` to `0.61`

for internal focusing telescope, `C=0.08` to `0.2`