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Kerr Cell Method

Kerr cell method is an improvement over the Fizeau’s toothed wheel apparatus. It was first devised by Gaviola in 1925. In place of the toothed wheel, electro optic shutter is used which is capable of chopping a beam of light several hundred times more rapidly than can be done by the toothed wheel.

Electro-optic shutter: It consists of a Kerr cell K placed between two crossed nicol prisms N₁ and N₂. Kerr cell is a small glass container having two electrodes filled with nitrobenzene. When a high voltage is applied to the electrodes of K, the light is transmitted through the system. On the other hand, when the field is switched off, the light is stopped and not transmitted through the system.

Thus, by using an electrical oscillator which supplies high frequency voltage, the beam of light can be interrupted at the rate of many millions of times in one second.

Karolus and Mittestadt at Leipzig in 1926 designed an arrangement similar to Fizeau.

Light from a source S after passing through the lens L₁ is made to pass through the nicol prism N₁ and it becomes plane polarized. This beam of light is focused at the centre of the Kerr cell K₁ and falls on the nicol prism N₂. This beam of light is rendered parallel by the lens L₂ and after reflection from the plane mirror M is allowed to fall on the lens L₃ which concentrates the beam in the middle of the Kerr cell K₂. Finally, the beam passes through the nicol prism N₃ and the lens L₄.

As the two nicol prisms N₁ and N₂ are crossed, no light reaches the mirror M and the eye. When a high frequency voltage is applied to the Kerr cell K₁ the beam reaches the mirror M and is reflected. As this reflected beam reaches N₂ after passing through K₂, it is again obstructed by N₃ and no light is observed by the eye. It should be remembered that N₂ and N₃ are crossed.

Suppose, a high frequency oscillatory voltage is applied to the Kerr cells K₁ and K₂ simultaneously such that there is no phase difference in their voltages. This means that the two cells will act as two shutters and are allowed to open and close simultaneously. Further, consider the light passing through the cell K₁ when the voltage is maximum and reaching the cell K₂, after some time when the voltage across the cell K₂ is minimum. Then no light reaches the eye.

Thus we find similar to Fizeau’s method, the arrangement N₁, K₁ and N₂ acts as a space for the passage of light while the arrangement of K₂ and N₂ acts as a toothed wheel for the observation of light.

If the distance between the two cells is d and ƒ is the frequency of H.F. voltage, then time taken by light to travel from K₁ to K₂

In this method,

ƒ = 3 × 10⁶ hertz

and the value of c was found to be 2.99778 × 10⁸ + 20 × 10³ m/s

Advantages: (1) As the frequency is very high, this device is capable of chopping a beam of light several hundred times more rapidly than can be done by the toothed wheel. Hence a shorter base line can be used.

(2) The apparatus can be set up in a laboratory.

(3) The accurate frequency of the high frequency oscillator is known.