102 Dr Searle, Experiments with a 'plane diffraction grating 



^ 



Equations (12), (13) with (7) give B^, C^, i/fg in terms of >Si, T^, W^, 

 which are given in terms of B^, C-^, i/j^ by (10). 



§ 4. ^ simple case. If we take C^ = 0, the incident wave front 

 is cylindrical. We then obtain 



^2 = Pi {F + 1 + (P - 1) cos 2i/ri}, Cg = 0, ...(14) 



or tan i/(2 = A;~^ . tan ^1 (15) 



The maximum difierence between i/j^ and 1^2 occurs when 



tan i/j-^ = k^, and then sin (i/^i — iff.^) = {k — 1 )/{k +1). 



Since C*2 = 0, the diffracted wave front is cylindrical. There is 

 therefore only one focal line at a finite distance from and this 

 distance is -Bg"-^. If the principal planes of the incident front are 

 turned round, i/j^ will change, so causing B2 to vary, and the 

 distance of this focal line from will vary. 



§ 5. Measurement of wave length. The results of § 2 can be 

 applied in the determination of the wave length of sodium light 

 by measurements made on an optical bench. On the bench slide 

 three carriages Z), H, K, as shown in plan in Fig. 3; D carries a 



horizontal glass scale divided in mm., H carries the grating G*- 

 (with vertical rulings), whose centre is 0, and K carries the con- 

 verging lens system L, of focal length/. At the end of the bench 

 is a vertical slit illuminated by a sodium flame F; to identify a 

 point E on the slit, a wire may be stretched across the slit. The 

 divided face of the scale faces the slit and this face and the plane 

 of the grating are perpendicular to the bench. The line through 

 the nodal points of L is parallel to the bench and passes through E. 

 The scale is first placed in the position A^B^, at a distance 

 from E exceeding 4/ by about 30 cm., and the lens is adjusted to 

 form a real undiffracted image on the scale at C^. The axial ray 

 of the incident beam is normal to the grating, and thus, if </> is 

 the angle between the normal and the axial ray of either diffracted 

 beam of order i, we have k"^ = sec^ <j). Since the incident beam 



