Dr Searle, Expervments with a prism of small angle 165 
_ strikes the face AB, some of it is reflected at that face and again 
falls on AC, where the greater part of it suffers refraction and 
passes out of the prism. If the angle of the prism is small enough, 
some of the light may suffer 4, 6,... internal reflexions, with 
corresponding emergent rays, but the light is so weakened at each 
reflexion that the images due to rays which have suffered more 
than two reflexions will not be easily seen unless the source of 
light is very powerful. 
The minimum deviation of a ray which suffers two reflexions 
is easily found. Let PQYRSTU (Fig. 10) be the ray. Since the 
path is symmetrical AQ = AT and AS= AR, so that SR makes an 
angle 42 with the normal to to at &. But the normal at & 
bisects SRY and hence QRT=4$7—-—41. Thus 
AQR=QRT-QAR=470 — 84, 
and hence the angle between RQ and the normal VQ at Q is 37. 
If TQH be a straight line, then PQH =4D’, where D’ is the 
deviation. Then the angle between PQ and the normal NQ is 
4D'+17%. Hence, by Snell’s law, 
STE) Fie) ane STN A Ntsc tion eee no oe (15) 
When 7 is so small that we can use the angles instead of their 
sines, we obtain 
1D) (CYC SD DEE Aa Late soanto stent (16) 
The minimum deviation (D) for a ray which has not suffered 
reflexion is approximately 
SD (oe DONA teh he hee Sai (17) 
From (16) and (17) we find 
ID Si) 
a 
and Cah DiS SD) eas ses EI (19) 
The measurements are carried out just as in § 6, using either 
a collimator or the auto-collimating device and a plane mirror. 
With »=3, the deviation D’ is seven times as great as D. 
A bright source of light will be required. Unless the inside of 
