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

51.—The natural law by which the power of refraction of any medium may be shown, and consequently the magnifying power of a lens in the ratio of its curvative through this refraction may be exemplified, is illustrated by the diagram on the following page (Fig. 1).

PP′, a line perpendicular to the surface of the plane of the medium (glass) with air above it, a ray of light would pass directly P to P′ through the glass surface SS′ without refraction, and so for all perpendicular incidences or emergences. By this perpendicular line PP′, termed the normal, all refractions are measured. The incident ray I to C is refracted to R. Then if we call the angle ICP I, and the angle RCP′ R, it is found by experiment that the perpendicular from I on PP′ (or sin I) bears a certain proportion to the perpendicular from R on PP′ (or sin R) according to the density of the glass. This proportion is generally expressed by the formula—sin I = µ sin R. Another incident ray I′ to C would be refracted to R′, and using similar notation to the above we have sin I′ = µ sin R′, and from this it follows that (sin I)/(sin R) = (sin I′)/(sin R′) = µ, which is called the index of refraction. Thus, if in a certain glass the sine of I measure 3 equal parts on any scale of length, and the sine R 2 parts on the same scale, the index of refraction of this glass would be 3 divided by 2 or 1·5.

Fig. 1.—Diagram of Refraction and Reflection.

Larger image

If the above process be reversed, and the ray of light R be refracted on passing from the glass to the air, it will be projected to I in the emergent ray, and follow the same law as that given above.

52.—Limit of Refraction—Reflection.—The sines to the angles ICP and I′CP′ being constantly greater in proportion to the obliquity in the case of glass we are considering by 1/3 than the sine of the angles RCP′ and R′CP′ of the rays of incidence thrown upward upon the surface SS′, it will be seen that at a certain angle or that in which the sine is 2/3 the radius, namely, 41° 48′ 37″, the equation given above makes sin I = 1 its maximum value; therefore, at any angle of incidence greater than this, the sine of refraction to continue in proportion would exceed the radius—an impossibility. The refraction, if possible, would carry the ray into the substance of the glass. This is therefore called the critical angle or angle of total reflection. At this point we may consider what must happen. By our rule, refraction must cease at the angle refraction becomes impossible by increase of sine, and as light cannot be extinguished in a transparent medium it must be reflected. Thus the ray r cannot be refracted in the proportion according to the rule given for sine I to sine R, as this would exceed the greatest sine, that is SC the radius, this ray will therefore be reflected at the surface from the point C, and pass in the direction r′. This property of refraction, continuing, as it were, into reflection, is made use of in many instruments.

53.—It may be worthy of repeating, as it is a mistake occasionally made by persons designing instruments for special purposes (as telemeters), that the refractions are not equal for varying angles of incidence, but only, as before stated, in the ratio of the sines. Thus there is no refraction P to P′ a certain refraction I to R, and a greater refraction I′ to R′, the refraction constantly increasing with the angle of incidence.

54.—The Reflection of Light follows a very simple law, viz.:—The angle of reflection of a ray of light from a reflecting surface is equal and opposite to the angle of incidence upon it. Thus, in Fig. 2, let a ray of light IA fall upon the reflecting surface SS′ at 30° of inclination to this surface, then this ray will be reflected from A to R at the angle RAS′, which is also 30°. If an object be at O, and the eye at I, then the object will appear as though it were at O′, as the eye only recognises the object in the direction from which it actually receives the light. The apparent angle S′AO′ is equal to IAS, so that the point of a mirror from which an object reflected is received is in direct line between the eye and the apparent object. This observation will be found useful in placing mirrors.