Foucault Rotating Mirror Method
In 1862, Foucault designed an apparatus for the measurement of the velocity of light. It requires again much shorter distance than Fizeau’s method and it is a modification of Fizeau’s method.
Foucault used a rotating mirror instead of a toothed wheel.
Light from a strong across S, falls on an achromatic lens L, after passing through the glass plate P. The light after passing through the lens will converge at the point I. If a mirror M1, is placed at A, light after reflection from the surface of the mirror M1, converges at the pole of the concave mirror C, whose distance from A is adjusted equal to its radius of curvature. Light is reflected back from C along its original path and finally the image is formed on the source S. As there is a half silvered glass plate P inclined at an angle of 45˚ to the axis of the lens, the image is formed at B1, which can be viewed with the help of a micrometer eyepiece.
Suppose, the plane mirror M1 is rotated rapidly at a uniform speed about an axis through A, the rays after reflection from the concave mirror C, find the plane mirror displaced by an angle θ to a position M2. The image is now observed at B2. The displacement B1B2 of the image is measured and the velocity of light is calculated.
Theory: Consider a point E on the concave mirror from which light is reflected back to the rotating mirror. When the plane mirror is at the position M1, the image of S is at I such that AE = AI = a, where a is the radius of curvature of the concave mirror. Thus, we find that A acts as the centre of curvature of the concave mirror. When the plane mirror is rotating with a uniform speed and is at a position M2, the image of S will be formed at I1 and the light appears to diverge from I1 instead of I.
If the mirror is turned through an angle θ, the reflected ray is turned through an angle 2θ:
I I1 = a × 2θ
As S and S1 are conjugate points with respect to I and I1, for the lens L
Suppose S1S = B1B2 = x
If the plane mirror makes π rotations per second, then the time taken by the plane mirror to rotate through an angle θ
= t = θ/2πn
During this time t, light travels from A to E and back again to A.
From (i) and (ii)
As n, a, d, x and b are measurable quantities, c can be calculated.
The displacement of the image in the Foucault’s experiment was only 0.70 mm and could be measured with the help of a micrometer eyepiece. The value of c found by Foucault was 2.98 × 108 m/s.
The main disadvantage of the Foucault’s method is that the image obtained is not very bright due to reflection and refraction of light at various surfaces.
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