axis of R. The lens L was placed as near as possible to R. The light
forming the return image lasts, in this case, while the first image is
sweeping over the face of the mirror, M. Hence, the greater the distance
RM, the larger must be the mirror in order that the same amount of light
may be preserved, and its dimensions would soon become inordinate. The
difficulty was partly met by Foucault, by using five concave reflectors
instead of one, but even then the greatest distance he found it
practicable to use was only 20 meters.

Returning to Fig. 1, suppose that R is in the principal focus of the lens
L; then, if the plane mirror M have the same diameter as the lens, the
first, or moving image, will remain upon M as long as the axis of the
pencil of light remains on the lens, and _this will be the case no matter
what the distance may be_.

When the rotation of the mirror R becomes sufficiently rapid, then the
flashes of light which produce the second or stationary image become
blended, so that the image appears to be continuous. But now it no longer
coincides with the slit, but is _deflected_ in the direction of rotation,
and through twice the angular distance described by the mirror, during
the time required for light to travel twice the distance between the
mirrors. This displacement is measured by the tangent of the arc it
subtends. To make this as large as possible, the distance between the
mirrors, the radius, and the speed of rotation should be made as great as
possible.

The second condition conflicts with the first, for the radius is the
difference between the focal length for parallel rays, and that for rays
at the distance of the fixed mirror. The greater the distance, therefore,
the smaller will be the radius.