length of a thick mirror 121 
Let K (Fig. 3) be a point on the front surface of the mirror near 
the vertex A. Let PK cut the principal plane HZin Z. Then, since 
the ray FZ passes through the focus /’, the corresponding emergent 
ray is parallel to the axis and, since Z is its own image, this 
emergent ray passes through Z. Hence the emergent ray is ZP, 
where ZP is parallel to the axis AF. Since the incident ray FK 
passes through K, the emergent ray ZP passes through the image 
of K, i.e. the image of K lies somewhere on ZP. Hence, an object 
AK of height a in contact with the surface AK has its image of 
height 6, where b= HZ. Since CA=p and CF=f, we have 
AF=p-—f, and thus 
GQ AW pai 
BTA i 
b 
Hence lire rate GOODDOHODUNCSOCOOOOOGNOG000 (7) 
In this method we are not concerned with the position of the 
image of K, but this image is at the point in which CK cuts ZP, 
since the incident ray CK becomes the emergent ray KC. 
Fig. 3. 
The measurements may be made by means of a microscope 
having a micrometer scale. The eyepiece is first adjusted so that 
the micrometer divisions are clearly seen. The two points A, K 
may be represented by two grains of lycopodium or by the vertices 
of two small cleanly cut triangles of tinfoil. If the surface of the 
mirror be breathed upon, the tinfoil will adhere to it. If the 
surface be convex, a glass scale may be used if it be placed with its 
divided face in contact with the vertex of the mirror system. 
Since the faces of the scale are parallel, the scale has no effect 
upon the number of micrometer divisions covered by either AK 
or its image. The microscope is then focused upon the two 
points so that there is no parallax between their images and the 
micrometer scale, and the reading of the micrometer scale is taken 
for each point. Let the difference of the readings be m. The 
microscope is then moved, without changing the distance between 
its object glass and eyepiece, so that it is focused upon the 
images of K and A, and the difference of micrometer scale 
