Page:Elementary Text-book of Physics (Anthony, 1897).djvu/422

408 $$AC$$ describe an arc tangent to $$Ar,$$ and from the same point as centre describe another arc $$r'r'$$ with a radius $$\mu \times Cy.$$ A tangent from $$A$$ to $$r'r'$$ is parallel to the emergent wave. It might be that $$A$$ would fall inside the arc $$r'r'$$ so that no tangent could be drawn. That would mean that there could be no emergent wave. The angle of incidence for which this occurs can readily be obtained. We have $$\frac{\sin i'}{\sin r'} = \frac{1}{\mu},$$ or $$\sin r' = \mu \sin i'.$$ Now the maximum value of $$\sin r'$$ is 1, which is reached when $$\sin i' = \frac{1}{\mu}\cdot$$ Any larger value of $$\sin i'$$ gives an impossible value for $$\sin r'.$$ The angle $$i' = \sin^{-1} \frac{1}{\mu}$$ is called the critical angle of the substance. For larger angles of incidence the light cannot emerge, but is totally reflected within the medium.

If a beam of white light be allowed to fall upon a prism through a narrow slit, it will be refracted, in general, in accordance with the law already given. The image of the slit, however, when projected upon a screen, appears not as a single line of white light, but as a variously colored band. This is due to the fact that the indices of refraction for light of different colors are different. Hence the index of refraction of a substance, as ordinarily given, depends upon the color of the light used in determining it, and has no definite meaning unless that color is stated.

335. Plane Mirrors.—The wave $$on,$$ represented in Fig. 98, is the same as would have come from a luminous point at $$C'$$ if the reflecting surface did not intervene. If this wave reach the eye of an observer, it has the same effect as though coming from such a point, and the observer apparently sees a luminous point at $$C'.$$ $$C'$$ is a virtual image of $$C.$$ When an object is in front of a plane mirror each of its points has an image symmetrically situated in relation to the mirror, and these constitute an image of the object like the latter in all respects, except that by reason of symmetry it is reversed in one direction.

336. Spherical Mirrors.—A spherical mirror is a portion of a