to 0/0 at normal incidence, but yield the correct results in the limit as . That they have opposite signs as we approach normal incidence is an obvious disadvantage of the sign convention used in this article; the corresponding advantage is that they have the same signs at grazing incidence. That completes the information needed to plot and for all angles of incidence. This is done in Fig.13, with in red and in blue, for three refractive indices. On the angle-of-incidence scale (horizontal axis), Brewster's angle is where (red) falls from 180° to 0°, and the critical angle is where both and (red and blue) start to rise again. To the left of the critical angle is the region of partial reflection, where both reflection coefficients are real (phase 0° or 180°) with magnitudes less than 1. To the right of the critical angle is the region of total reflection, where both reflection coefficients are complex with magnitudes equal to 1. In that region, the black curves show the phase advance of the p component relative to the s component: It can be seen that a refractive index of 1.45 is not enough to give a 45° phase difference, whereas a refractive index of 1.5 is enough (by a slim margin) to give a 45° phase difference at two angles of incidence: about 50.2° and 53.3°. This 45° relative shift is employed in Fresnel's invention, now known as the Fresnel rhomb, in which the angles of incidence are chosen such that the two internal reflections cause a total relative phase shift of 90° between the two polarizations of an incident wave. This device performs the same function as a birefringent quarter-wave plate, but is more achromatic (that is, the phase shift of the rhomb is less sensitive to wavelength). Either device may be used, for instance, to transform linear polarization to circular polarization (which Fresnel also discovered) and vice versa. In Fig.13, is computed by a final subtraction; but there are other ways of expressing it. Fresnel himself, in 1823, gave a formula for . Born and Wolf (1970, p.50) derive an expression for and find its maximum analytically. For TIR of a beam with finite width, the variation in the phase shift with the angle of incidence gives rise to the Goos–Hänchen effect, which is a lateral shift of the reflected beam within the plane of incidence. This effect