The telescope and the theodolite

The theodolite is the principal instrument employed for the measurement of angles in surveying. The telescope is an essential component not only of the theodolite but also of the level and of modern miner’s dial, and has the same essential function and design in each.

The simplest refracting telescope used in surveying instruments consists of two co-axial lenses, the object-glass A and the eyepiece B. The object-glass is always a convex lens and is directed towards the distant object. Its function is to collect rays emanating from the distant object. These rays, on passing through the object-glass are refracted as shown and pass on to the eyepiece by which they are further refracted into the eye.

Figure shows the principle of the Kepler type of telescope used in surveying where quantitative measurements must be made. The position of any point in an image I₁ M₁ may be determined by taking any two rays from the corresponding point viewed, say Y; one ray YP parallel to the principal axis of the lens, is refracted through the centre of curvature F, of the lens; the other ray YO passes through the centre of the lens and in a thin lens passes on unrefracted. The intersection of these two rays determines the position of the image of the point. The rays of light are thus brought to a focus before they enter the lens forming the eyepiece B, resulting in the formation of a “real” inverted image I₁ M₁ in front of the eyepiece. The eyepiece lens B is so placed that the image formed by the object-glass lies at a distance from it less than its focal length KF. Intersection of two such rays as above mentioned can then only be effected by extending the rays backwards to from a “virtual” inverted image, I₂ M₂. This is so called because the real image I₁ M₁ as viewed through the eyepiece only appears to emanate from the position I₂ M₂ and does not actually exist there in space. Note that the image is magnified by the eyepiece, the function of which is to bring the very small “real” image close to the eye so that it appears larger.

4.Answer the following questions:

1. What is a theodolite?

2. What is shown in figure?

3. What device is the telescope an essential component of?

4. What parts does the simplest telescope consist of?

5. What is the function of an object-glass?

Complete the sentences with the following words

A theodolite, an object-glass, to invert, to magnify, an eyepiece, a convex lens, a distant object, to collect, measurements, rays.

6. Read the text once more and find following translations of word expressions:

1. необходимый компонент.

2. удаленный объект.

3. исходящие лучи.

4. неотраженный луч.

5. пересечение двух лучей.

6. обратное изображение.

Lesson 10

1. Give definitions to the following words:

Horizontal, vertical, length, distance, line, angle.

2. Read and translate the text into native language:

Measurement of Dimensions

Four dimensions are measured: horizontal lengths, vertical lengths, horizontal angles, and vertical angles. A horizontal length is the straight line distance measured in a horizontal plane. In most cases a distance measured on a slope is changed to its horizontal equivalent. Measurements are made by direct and indirect methods. Direct measurements are made by wheels, human pacing, and tapes of cloth, metallic cloth, or steel. Indirect measurements are made by use of stadia-equipped instruments and graduated rods or by electronic distance-measuring equipment. The type of measurement and equipment used depends on required accuracy, access to the line, and the time and cost involved.

A vertical lengthis a measurement of a difference in height or elevation. Measurements can be made by an altimeter, which indicates barometric pressure; by a transit; or by plumb line and tape for short vertical distances. In most cases remoteness of points and accuracy require indirect measurements with instruments such as the level and graduated rod.