Modification of Newton's Rings. 285 



that if i and <' are small, i being < <', this is minimum when 

 2 jTcos i'+ B = 0, or = x, or =2X, &c. and maximum when 



27 , cosi' + J B=^, or =^, &c. : 

 2 2 



and that this continues till « + i' = 90°: but as soon as « + «' exceeds 

 90°, the expression is maximum when 2 T cos «' + B = 0, or = x, or 

 = 2X, &c, and minimum when 



2rcos<' + J B= g, or = y-. &c. 



If i? be small, the first of these represents rings similar to 

 Newton's reflected rings, and the second represents rings similar 

 to his transmitted rings. 



If the light is polarized in the plane of reflection, the ex- 

 pression for the displacement in light reflected from the lower 



surface of the glass is a . -. — r — l -r- , which does not change sign 



° sin (i + i) ° 



like the former: and a similar train of reasoning shews that the 

 character of the rings which it produces will not suddenly change. 

 If the light is polarized in a plane inclined by the angle 

 a to the plane of reflection, we must regard this as consisting 

 of two vibrations, one perpendicular and one parallel to that 

 plane, whose proportions are cos a : sin a. The original vibration 

 perpendicular to that plane must now be taken 



a . cos a . sin — — (vt—z), 

 X 



and that parallel to the plane 



a. sin a .sin — (vt—z). 

 x 



