2TacheometerTacheometer is transit theodolite fitted with stadia diaphragm, and analltic lensAnallatic lens: Additional convex lens is provided between the eye piece and the object glass at a fixed distance from the object glass. The purpose of providing anallatic lens is to make additive constant (f+d) exactly zero.
3Advantage Disadvantage Anallatic lens is provided in external focusing telescope, not required in internal focusing telescope.Advantageit simplifies the calculation by making the additive constant ‘0’.Therefore, there is only one constant which is multiplying constant.Distances are directly calculated by multiplying the difference of stadia hair readings by 100.DisadvantageBrightness of the image is much reduced due to absorption of light.
4Principle of tacheometry The principle of techeometry is based on property of isoscales triangles, where the ratio of distance of the base from apex and length of the base is always constant.D1/S1=D2/S2=D3/S3=f/I (multiplying constant)F= focal length of object andi= stadia intercept
7The stadia readings with horizontal sight on a vertical staff held 50 m from a tacheometer were m and m. the focal length of the object glass was 25 cm. the distance between the object glass and the vertical axis of the tacheometer was 15 cm. calculate the stadia interval.
8Theory of anallatic lens NotationS = staff intercept CD1O= Optical centre of object glassA= Optical centre of anallatic lensV= vertical axis of inst.P= Principal focus of the anallatic lensf1 and f2= conjugate focal lengths of the object glassf= focal length of object glassf’= focal length of the anallatic lensK= distance between object glass and anallatic lensd= distance between optical centre of object glass and vertical axis of instrumentM=distance between optical centre of object glass and real image dci= length of real image dc, when anallatic lens is providedI’= length of real image d3c3, when anallatic lens is not providedD= distance between vertical axis of instrument and the staff
9Home assignment (no need to submit): How does the an anallactic lens work to reduce the additive constant to zero?Illustrate the working of anallactic lens by a neat diagram and discuss the effect on constants using appropriate expression?Derive the distance and elevation formulae for following cases of tachometry.Inclined sight and staff vertical (for angle of elevation and depression both)Inclined sight and staff normal (for angle of elevation and depression both)