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Focal Lines

When light falls obliquely on a convex lens a refracted pencil does not converge to a point, but to two focal lines in planes at right angles. Let us suppose the lens placed normal to the incident light which is travelling in a horizontal direction, and then turned about a vertical axis till the angle of incidence is φ, then the primary focal line is vertical, the secondary is horizontal, and if u be the distance of the source of light from the lens, v1, v2, the distances of the focal lines, supposed to be real, and/the focal length of the lens, we have(1)

If, then, we determine v1 and v2 this equation will give us the value of φ, and if the apparatus can be arranged so that φ can readily be measured, the comparison of the value given by the formula with the result of the measurement enables us to check the formula.

To measure φ, the stand carrying the lens should be capable of rotation about a vertical axis, and a horizontal circle attached to it so that its centre is in the axis. A pointer fixed to the moving part of the stand turns over the circle. The reading of the pointer is taken when the lens is placed at right angles to the light, and again when it has been placed in the required position. The difference between the two gives the angle of incidence. To find v1 and v2, it is best to use as object a grating of fine wire with the wires vertical and horizontal, and to receive the light after traversing the lens on a screen of white paper. For one position of the screen the vertical lines will appear to be distinctly focussed, while the horizontal are hardly visible. The screen then is in the position of the primary focus, and the distance between it and the lens is v1. For a second position of the screen the horizontal lines are in focus and the vertical are not seen. This gives the secondary focus, and we can thus find v2.

Each observation will require repeating several times, and in no case will the images formed be perfectly clear and well-defined. A very good result may, however, be obtained by using the homogeneous light cf a sodium flame behind the gauze, and receiving the image upon a second gauze provided with a magnifying lens, as described in 53.

Experiment. - Light falls obliquely on a lens; determine the position of the primary and secondary foci, and, hence, find the angle of incidence.

Enter results thus:

(1) See Parkinson's Optics, p. 101. The sign of u has been changed.

Last Update: 2011-03-27