Dr Searle, Experiments with a plane diffraction grating 103 



corresponding to the point E of the slit is stigmatic, the vertical 

 focal lines of the diffracted beams of order i will be at a distance 

 OCJk^ from 0, along lines OPj, 0^^, each making an angle cf> 

 with 0C\. Sharp images of the slit will pass through P^, Q^ and can 

 be focussed on the scale if it is moved to A\By' . With the grating 

 used in § 9, the two sodium lines can easily be separated. Then 

 sin (/) = ^PiQi/OPj^. Since OP^ is difficult to measure, we suppose 

 OX-^ known, where Z^ is the mid-point of PiQi- If OX^ = x-^, 

 P^Q^ = 2;yi, tan <^ = iPiQJOX, = yjx^. 



The glass plate protecting the grating prevents an accurate 

 measurement of OX^. We therefore move the lens carriage along 

 the bench so that the undiffracted image is focussed on the scale 

 at C'g. If the scale is moved further towards 0, the difPracted 

 images can be focussed at Pg? Q2- If OX2 = x^, ^2^2 ^ '^Ih' 

 tan (j) = y^l^o,- Hence 



tan (j,^{y^- y,)l{x^ - x^) (16) 



Putting 6-1^ = 0, $2 = (f) in (6), we find 



X = d sin (jiji, (17) 



where i is the order of the image and d is the grating interval. 

 From (16) and (17), A is determined. 



Since it is an angle we measure, small errors of focussing will 

 be of little account, for, in spite of them, the point in which the 

 axial ray cuts the scale in each case will be correctly estimated, 

 and this is all that is necessary. 



§ 6. Test of laiv of obliquity. Let OCj = u^, OC^ = ^2' ^Pi = ^'i) 

 OP2 ^ V2- Then v^ — v^ = [{x^ — x^)^ + (y^ — y^fY- But, since 

 ^2= sec^^, we have, by § 5, u^ = u-^ cos^ (J3, v^ = U2 cos^ ^, and 

 thus i\ — V2= (w^ — Mo) cos^ cf). Since Mj — Wg is known from the 

 bench readings, we can test the law for the vertical focal lines 

 by comparing the two values of v^ — ?',• As we are now concerned 

 with the positions of images the focussing must be accurate. 



If the slit is not too narrow, the diffracted images of order i 

 of the horizontal wire stretched across it may be focussed on the 

 scale. If these are at jOj, q^^ when OC = ^^ and at ^03, q2 when 

 OC = ^2, and if p^q^^ = 2r]^, ^2^2 = ^772, then 



ViP2 - mi - Q' + (^1 - ^2)']^. 



Since, by § 2, 1^= T^, we have p^2 = '^h ~ ^'2- The two values 

 of PxP2 are compared. 



It is difficult to obtain satisfactory readings for x and ^. This 

 is largely due to the fact that the diffracted rays in the horizontal 

 plane through do not meet in a point but touch a caustic of large 



