Radiation Pressure. 401 



If there is total refraction, let AB (fig. 5) be refracted 

 along BC. If E is the energy in unit length of AB, and if 

 E' is the energy in unit length of BC, the equality of energy 

 in the two beams is expressed by 



VE = V'E'. 



But if M is the stream of momentum passing per second 

 along AB, and if M' is that along BC, 



M = E and M' = E'. 



Whence VM = V / M / 



and M / = y / M = ^M. 



Let AB=M, and BC along the refracted beam =M/ 

 =jiM=/AAB. 



Draw CD parallel to BA, meeting the normal BN in D. 

 Then pR 



CD = CB sin r/sin i = — = AB = M. 

 A* 



Hence by the refraction, momentum DC has been changed 

 to momentum BC, or momentum BD has been imparted to 

 the light. There is therefore a reaction DB on the surface- 

 The force DB may be regarded as a pull-out or a pressure 

 from within, and it is along the normal *. 



If the refraction is from a denser to a rarer medium, CB 

 will now represent the incident stream and BA or CD the 

 refracted stream. BD is the stream added to CB to change 

 it to CD, and DB is the force on the surface, again a force 

 outwards along the normal. 



In any real refraction with ordinary light, there will be 

 reflexion as well as refraction. The reflexion always pro- 

 duces a normal pressure, and the refraction a normal pull. 

 But with unpolarized light, a calculation shows that the 

 refraction pull, for glass at any rate, is always greater than 

 the reflexion push, even at grazing incidence. 



The following table has been calculated from Fresnel's 

 formula for unpolarized light by Dr. Barlow : — 



* It has "been pointed out by J. J. Thomson, ' Electricity and Matter,' 

 p. 07, " that even when the incidence of the light is oblique, the momentum 

 communicated to the substance is normal to the refracting surface." The 

 change of momentum of a beam of light is, it may be noted, the same on 

 the wave and on the corpuscular theory. 



