b) Show that superposition of two linearly polarised light waves having different amplitudes and a finite phase difference can be used to produce elliptically plane polarised waves.
When two linearly polarized light waves with different amplitudes and a finite phase difference superpose, the resulting wave can exhibit elliptical polarization. Here's how we can show that:
Consider two light waves with electric fields described as:
E1=E10cos(ωt+ϕ1)E_1 = E_{10} \cos(\omega t + \phi_1)
and
E2=E20cos(ωt+ϕ2)E_2 = E_{20} \cos(\omega t + \phi_2)
where E10E_{10} and E20E_{20} are the amplitudes of the two waves, ω\omega is the angular frequency, and ϕ1\phi_1 and ϕ2\phi_2 are the initial phase angles of the two waves.
The phase difference between the two waves is given by:
Δϕ=ϕ2−ϕ1\Delta \phi = \phi_2 - \phi_1
The electric fields of the two waves can be written as vector sums, considering that they are linearly polarized and
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