Dr Searle, Experiments with a prism of small angle 161 
§5. Determination of the angle and refractive index of a 
prism by aid of a liquid of known index. In the last experiment 
no assumption was made as to the magnitude of the angle of the 
prism. In the following experiment, however, in order to simplify 
the mathematics, it is necessary that the angles concerned should 
be “small.” 
We shall first calculate the deviation when a ray passes with 
small angles of incidence and refraction from air into a medium of 
index p. Let PQR (Fig. 6) be a ray making angles 6 and $ 
Fig. 6. 
with the normal MQN in the air and in the medium. Then 
sn@=psing. But 
Tet alice 168} 
= Say Aes 3 
@=sin@+ 5.5 sin O+ 5 
and sing@= ¢—1¢', as far as d’*. Hence, to this order, 
d= ysin $+ 5 (usin $) =n (>— 49!) + Lug" 
ange seo (3) 
Ente Uist G. an ay (4) 
If the deviation be D, we have D = 6@-— ¢, and thus 
1D) SC 1) Se GPS) OP. escacot once»: (5) 
Next consider the passage of a ray in a principal plane through 
a prism of index mw and of small angle 7. If the ray passes through 
the prism symmetrically, the angles which it makes in the medium 
of index w with the two normals are each 47. If the path PQRS 
(Fig. 7) is unsymmetrical, these angles will be 42+ and 47 — », 
Fig. 7. 
where 7 is the angle between the unsymmetrical path and a 
symmetrical path in the medium. For the refraction at Q, where 
the value of ¢ is 47+, we have, by (5), 
D,=(u—1) Git) + uel Gitay, 6) 
