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# On Optical Measurements

Many of the simpler optical experiments described below depend on the determination of the positions of some luminous object and its. real image formed after reflexion or refraction. A formula is obtained expressing the quantity sought for, e.g. the focal length of a lens, ia terms of distances which can be readily determined. These are measured and their values substituted in the formula; the value of the quantity in question is determined by calculation.

Now, in almost every case, the formula is one giving the relation between the position of a point and its geometrical image, and to obtain this the assumption is made that we are only concerned with a small pencil, the axis of which is incident directly on the reflecting or refracting surfaces.

If this be not the case, there is no such thing as a point image of a point. The rays diverging from a given point of the object do not all converge again exactly to one and the same point For each point in the object we have - supposing still that the incidence is direct - a least circle of aberration through which all the rays from that point pass, and the nearest approach to an image is the figure formed by the superposition of all these least circles of aberration, which will be a representation of the object, more or less blurred, and differing in position from the geometrical image.

Now, frequently this happens with the images produced by the optical combinations with which we shall have to do. The pencils which go to form the various images are not small pencils incident directly, and the phenomena are thus complicated by the effects of aberration.

Thus, for example, we may require the radius of a concave mirror, three or four inches across and six or eight inches in radius; or we may be experimenting with a lens of an inch or so in diameter and only one or two inches in focal length. In both these cases we should meet with aberration difficulties. We shall see best how to allow for this in each separate experiment

There is one measurement common to many optical experiments, the mode of making which may best be described here.

Two objects - the one may be a lens, the other a screen on which an image is focussed - are attached to the supports of an optical bench described below. This is graduated, and the supports possibly are fitted with verniers; at any rate, there is a mark attached to them, the position of which, with reference to the scale of the bench, can be found.

We can thus find easily the distance between the two fixed marks on the supports; but suppose we require the distance between the screen and one face of the lens. To obtain this we must know their positions with reference to the fixed marks. Now, the apparatus is generally constructed so that the central plane of the lens and the plane of the screen respectively are in the same vertical plane as the marks in question, so that, neglecting the thickness of the lens, the distance between the marks is, as a matter of fact, identical with the distance required. But for some purposes this is not sufficiently accurate. We may, for example, wish to consider the thickness of the lens in our measurements.

In this case, take a rod with two pointed ends, and measure carefully its length. Let it be a. Put one end against the screen and move up the support carrying the other surface, until this is in contact with the other end of the rod. Let the distance between the marks on the supports, as read at the same time by the sgale and vernier, be b. Then, clearly, if in any other position of the supports the distance between the marks on them is c, the distance between the surfaces is c+a-b, for a was the distance between them in the first position, and c-b is the distance by which it has been altered.

We may make the same measurement by the following slightly different method which can be used conveniently for determining the distance between two objects measured parallel to any fixed scale. Fix securely to the vernier of the scale a stiff piece of wire, and bend it until its end comes in contact with one of the objects in question, and read the vernier. Now move the vernier with the wire fixed relatively to it, along the scale, until the same end of the wire comes in contact with the second object, then read the vernier again. The difference between the two readings is the distance required.

This will be found a convenient way in making the measurements, described in §49, if the mirror can be fitted to one of the supports of the optical bench.

Of course, if the distance required be only small, the simplest method of all is to use a pair of compasses and take it off along a finely divided scale.

Last Update: 2011-03-27