INTERFERENCE COLOURS OF THIN PLATES. 245 



3. INTERFERENCE OF KEFRACTED AND DIRECT LIGHT. 



The deflexion of incident rays towards a directly 

 illuminated point p of the plane of adjustment 

 (Fig. 135) may be produced as well by refraction 

 as by reflexion, and since the refracted ray always 

 travels over a longer path than the direct one, 

 interference must then take place. It is not 

 always easy to distinguish whether the refracted 

 or the reflected rays are those which interfere 

 with the direct ones, since the inclination of the 

 reflecting or refracting surfaces, the refractive 

 ratio, &c., in fact the necessary data for the deter- 

 mination of the path of the rays, in many cases 

 cannot be ascertained. 



4. INTERFERENCE COLOURS OF THIN PLATES. 



If a thin layer of air is enclosed between two refracting media, 

 for instance, between a plate of glass and a convex lens of very 

 shallow curvature, interference colours are produced which are 

 usually termed Newton's rings. The interference takes place 

 between the rays reflected at the upper and those reflected at 

 the lower bounding surface of the layer of air. Since the latter 

 have travelled over a longer path, they are on emergence generally 

 displaced, as compared with the former, by a larger or smaller 

 fraction of a wave-length. If the displacement, assuming the light 

 to be homogeneous, amounts to half a wave-length, or an odd 

 number thereof, the two systems of rays annul each other, and the 

 corresponding part appears dark ; in every other case a greater or 

 less degree of brightness is produced, which reaches its maximum 

 with a difference of phase of one entire wave-length. 



The same phenomena are also produced by any thin layer of a 

 liquid or solid substance, provided the incident light is reflected at 

 both the bounding surfaces as just described. For estimating these 

 effects of interference the fact is important, that by the reflexion 

 half a wave-length is lost if the second medium is denser than the 

 first, whilst the phase remains the same if the contrary is the case. 



