Question

How are Lissajous figures formed? How can we apply the same concepts to the polarization of light?

Answer 1

Lissajous figures are the resultant path traced out by particle when it is acted upon simultaneously by two simple harmonic motions at right angles to each other.

The nature of resultant path depends upon:-

1)The amplitudes of vibrations

2)The frequencies of two vibrations

3)Phase diffeerence between the vibrations

The lissajous figures can be applied in the polarisation of light to trace the path difference (or) phase difference between the polarised lights and to determine the resultant path of the polarised lights.

For example if,we consider the vectors formation of polarised lights as

Ex=E0xcoswt

Ey=E0ycos(wt+p)

where p is the phase difference

By, the above relations we are able to observe the three types of formations such as ,a linear polarisation is obtained of the relative phase is set 00 to 1800 an ellipitical polarisation.An ellipitical polarisation will result for the relative phase of 900to 1800 and the circular polarisation can be also obtained by the same phase.These,illustrates the influence of the phase difference on the resulting lissajous figures of fixed,non-equal amplitudes.

In the lissajous figures the is no alternation if the sign of the phase shift is changed.This is not exactly true in terms of polarisation an electromagnetic wave addind a time axis to the lissajous figures helps to clarify the relevance of the phase sign.

  

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