Fig. 48.—Experimental Proof that the Angle of Incidence = Angle of Reflection.
In order to find the direction of the reflected luminous rays, we must turn the telescope on its axis, until the rays reflected by the surface of the mercury bath enter it and produce an image of the star. When the image is brought to the centre of the telescope, it is found that the angle R´ I´ N´ is equal to the angle of reflection N, I, R. Thus, in reading the measure on the graduated circle of the theodolite the angle of reflection can be compared with the angle of incidence.
Now, whatever may be the star observed, and whatever its height above the horizon, it is always found that there is perfect equality between these angles. Moreover, the position of the circle of the theodolite which enables the star and its image to be seen evidently proves that the ray which arrives directly from the luminous point and that which is reflected at the surface of the mercury are both in the same vertical plane.
Now this demonstrates one of the most important laws of reflection. The laws of refraction do not deal directly with the angles themselves, but with the sines of the angles; in reflection the angles are equal; in refraction the sines have a constant relation to each other.
So far we have dealt with plane surfaces, but in the case of telescopes we do not use plane surfaces, but curved ones, so we will proceed at once to discuss these.
Fig. 49.—Convergence of Light by Concave Mirror.
Fig. 50.—Conjugate Foci of Convex Mirror.