Surveying and Levelling Instruments, Theoretically and Practically Described. / For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field.

by William Ford Stanley

Fig. 2.—Diagram reflections from a plane.

Fig. 3.—Reflection from a prism.

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55.—Prismatic Reflection. The same law as given above applies to internal reflection from glass. Let Fig. 3 represent the section of a prism ff′, two plain surfaces of glass at right angles to each other, and the third side making an angle of 45° with each of the other two. The ray i will therefore pass perpendicularly through the plane f without refraction to meet the plane 45° and the angle of reflection, being equal to the angle of incidence, will leave this plane at 45°, and reach r. The angle of glass here given of 45° being greater than 41° 49′, its extreme angle of refraction, the internal reflection will be therefore perfect.

56.—Prismatic Reflection, as this is termed, is largely used in optics in preference, where practicable, to open reflecting surfaces, from the certainty of keeping the reflecting surface clean; as dirt exterior to the reflecting surface of the prism does not affect the internal reflection in any degree.

57.—The reflection is shown for clearness from the plane (Fig. 2) as it actually occurs, or as it is measurable, independent of theory. In optics it is found much more convenient to take the reflection in relation to an imaginary line drawn perpendicular to the plane. In Fig. 4 NA is termed the normal. Taking the angles as before as 30° to the plane, the optical expression of this would be 60° to the normal, and the reflection of the incident ray IA to R would be in the angle IAR 60° + 60° = 120°, the amount the incident ray is deflected from its former course. This principle is important to be understood in the construction of the sextant and other reflecting instruments. In reflection the ray is found to follow the shortest path,—that is, the path I to R by reflection is shorter in the lines IAR, placed at equal angles to the normal, than it would be by any other possible path. As, for instance, it is shorter than IaR, shown by dotted lines.

Fig. 4.—Measurement of angle of reflection in optics.

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