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Anderson Light Method

In 1941, W.C. Anderson made use of one Kerr cell and divided the transmitted light pulses into two beams by means of a half silvered glass plate. His arrangement is shown in fig. Light from a source S is allowed to pass through a modulated Kerr cell and is split up into two beams by the half silvered glass plate M₁. One beam of light goes towards M₂ and is reflected back, and the other beam goes along a longer path towards M₃, M₄, M₅ and M₆ and after reflection from M₆ retraces its path and finally the two beams reach the photoelectric cell P.

If the longer path exceeds the shorter path by [(2a + 1)λ]/2 the resultant of the two modulated waves reaching the photocell will give a constant intensity. The amplifier connected to the photo-cell will give zero response in this case.

After, light after reflection from M₃ is allowed to fall normally on M₄ and it retraces its own path towards M₁. This is done for cutting the light to go to M₅ and M₆. The position of the mirror M₂ is adjusted so that again there is zero response in the amplifier connected to the photocell. If the extra path (M₄ to M₆ and back) is a whole number of λ, no charge in the response of the photo cell is observed.

In the actual experiment the extra path was found to be equal to 11 λ.

Here, x = distance from M₁ to M₄ and back

y = distance from M₁ to M₂ and back

S = distance from M₄ to M₆ and back

δ_x = the distance between M₄ and M₄’

δ_y = the distance between M₂ and M₄’

In the first case the path difference

(x + S) – y = (2n + 1) λ/2                      (i)

and in the second case the path difference

(x + 2δ_x) – (y + 2δ_y) = λ/2                     (ii)

Subtracting (ii) from (i)

S + 2δ_y – 2δ_x = nλ                                 (iii)

It was found that n = 11

∴ λ can be known from equation (iii)

∴ c = λ/T                                              (iv)

where, T = 1/ƒ

Here, ƒ is the frequency of H.F. oscillator connected to the Kerr cell and this can be accurately known.

The value of c found by Anderson by this method = 299.776 ± 6 km/s.

This value is the mean of 2895 observations made by Anderson.

Advantages: (1) The use of two Kerr cells is avoided in the method because it is practically difficult to match the characteristics of the two cells.

(2) The observations are taken by a photo cell instead of the eye.

Source of error: The main source of error in this method is the difficulty in arranging for both beams to use the same position of the photoelectric cell.