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Thermodynamics

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Piezoelelectric Grazing

When a quartz is subjected to a high frequency electric field it is alternately compressed and extended and thus high frequency oscillations are set up. This effect is known as piezoelectric effect. When these high frequency oscillations are set up in the form of pulses in a quartz crystal, it will be crossed by several parallel nodal planes. In such a case the intensity and refractive index at nodal planes is different from those at other planes and thus the crystal will act as a diffraction grating.

Monochromatic light from a source S is allowed to fall on the quartz crystal C (whose faces are cut parallel) after reflection from the glass plate M. The lens L is used to make the beam parallel. As mentioned, the quartz crystal will act as a grafting. Therefore, light after passing through the crystal passes through the slit A of the screen. Finally it is brought to focus by the lens L₁, Convex lens L₁ and concave mirror B are fixed at the two ends of a tube such that the length of the tube is equal to the focal length of the lens L₁ and also equal to the radius of curvature of the concave mirror B.

The light retraces its own path and on arriving at the quartz crystal C if it finds the crystal exactly in the same condition as on its forward journey, then the image of S is seen by the eye. If on the other hand the light on arriving at the crystal C finds that the crystal is not exactly in the same condition as on its forward journey, no image of S is seen by the eye.

Therefore quartz crystal C acts similar to a toothed wheel in Fizeau’s method on Kerr cell in Anderson’s method.

Let the frequency of oscillations be ƒ. Then the rate of formation of the grating is 2ƒ per second. Therefore, when the image is seen by eye, the time taken by light to go from C to B and back is a simple multiple of 1/2ƒ.

The tube containing L₁ and B is moved away from the screen along CB. At first it is observed that the image disappears. It again reappears when the tube reaches some position B’. this will be so, when the distance BB’ and back (i.e. 2d) is travelled by light in the time 1/2ƒ second. Several such points can be located when the tube L₁B is moved away from the screen which are d cm apart from each other. For accuracy the mean of all these distances is taken and let it be equal to d.

In the actual experiment performed by Houston, the value of ƒ was equal to 115 × 10⁴ hertz.

The value of c calculated by Houston in vacuum = 299.782±9 km/s, which agrees with the results obtained by other methods.

Example: In Houston’s Piezoelectric experiment, the image of the source could be observed when a tube containing the mirror and the lens was at a certain position. The image of the source was again observed when the tube was moved 65 cm away from the screen. If the crystal was placed in a high frequency electric field of frequency 115 × 10⁴ hertz find the velocity of light.

c = 4 d ƒ

Here, ƒ = 115 × 10⁴hertz

d = 65 cm

∴ c = 4 × 65 × 115 × 10⁴

c = 2.99 × 10¹⁰ cm/s = 2.99 × 10⁸ m/s.