ON THE ELEMENTARY THEORY OF OPTICAL INSTRUMENTS. 239 



point of the object before incidence passes through the corresponding point of 

 the image after emergence, and this determines one point of the emergent ray. 

 If at any other distance from the instrument a plane object has an accurate 

 image, then there will be two other corresponding points given in the incident 

 and emergent rays. Hence if we know the points in which an incident ray 

 meets the planes of the two objects, we may find the incident ray by joining 

 the points of the two images corresponding to them. 



It was then shewn, that if the image of a plane object be distinct, flat, and 

 similar to the object for two different distances of the object, the image of any 

 other plane object perpendicular to the axis will be distinct, flat and similar 

 to the object. 



When the object is at an infinite distance, the plaile of its image is the 

 principal focal plane, and the point where it cuts the axis is the principal 

 focus. The line joining any point in the object to the corresponding point of 

 the image cuts the axis at a fixed point called the focal centre. The distance 

 of the principal focus from the focal centre is called the principal focal length, 

 or simply the^bcaZ length. 



There are two principal foci, etc., formed by incident parallel rays passing 

 in opposite directions through the instrument. If we suppose light always to 

 pass in the same direction through the instrument, then the focus of incident 

 rays when the emergent rays are parallel is the first principal focus, and the 

 focus of emergent rays when the incident rays are parallel is the second 

 principal focus. 



Corresponding to these we have first and second focal centres and focal 

 lengths. 



Now let (?! be the focus of incident rays, P 1 the foot of the perpendicular 

 from (?j on the axis, Q t the focus of emergent rays, P 3 the foot of the corre- 

 sponding perpendicular, F^ the first and second principal foci, A^A^ the first and 

 second focal centres, then 



lines being positive when measured in the direction of the light. Therefore 

 the position and magnitude of the image of any object is found by a simple 

 proportion. 



