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55.There is a remarkable exception or modification to this rule in the case of combustible substances, (in which the diamond is included) which always refract much more than other substances of like densities, that is, in cases when the inclination of a ray to the perpendicular is diminished by the refraction, it becomes less for a combustible, than for an incombustible substance, but when the angle of refraction is greater than the angle of incidence, it is less increased in passing into a combustible, than into another substance of equal density.
56.Between media of equal refracting powers there is no refraction, and in general the superiority of action of one medium over another is well expressed by the invariable ratio of the sines of incidence and refraction, when a ray passes from one into the other.
57.We may here take occasion to observe that since when a ray of light passes out of a denser into a rarer medium, that is, out of one of a stronger into one of a weaker refracting power, the angle of refraction is greater than that of incidence, there is some angle of incidence for which the angle of refraction is a right angle (v. Fig. 55.) Past that point there can be no refraction, for though we might fancy an angle of incidence greater than a right angle, there is no angle whose sine is greater than the radius.
For instance, when a ray of light passes out of glass into air, the ratio of the sines of the angles of incidence and refraction is about 2 to 3. Here then we have sinφ=23sinφ′, or sinφ′=32sinφ, and since sinφ′ can not exceed 1, sinφ cannot be greater than 23, or φ greater than 41° 49′.
The fact is, that when the angle of incidence in the denser medium exceeds the proper limit, the light is reflected instead of being refracted, as may easily be seen by holding a glass of water above one's eye, when it will be observed that any rays of light coming from below so as to make with the surface an angle of less than 41° 24′, which in this case is the complement of the limiting angle of incidence, are strongly reflected.
This leads us to remark that as the limiting angle of incidence out of fresh water into air, is about 48° 36′, an eye placed in water,
