Consider a beam of plane polarised light of wavelength λis inci...
For quarter wave plate
n = 0,1,2, 3.......
When a plane polarised light is incident on quarter wave plate with angle θ= 45° then output light is circularly polarised.
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Consider a beam of plane polarised light of wavelength λis inci...
Λ and intensity I incident on a polarizer. The polarizer transmits only the component of the electric field vector that is parallel to its transmission axis. Let's assume that the transmission axis of the polarizer is aligned with the x-axis.
The electric field vector of the incident light can be written as E0*cos(ωt), where E0 is the amplitude of the electric field and ω is the angular frequency of the light.
The transmission axis of the polarizer is aligned with the x-axis, so it only transmits the component of the electric field vector that is parallel to the x-axis. Therefore, the transmitted electric field can be written as E0*cos(ωt) * cos(θ), where θ is the angle between the incident electric field vector and the x-axis.
The intensity of the transmitted light can be calculated using the formula I_transmitted = (1/2)*ε_0*c*E_transmitted^2, where ε_0 is the vacuum permittivity, c is the speed of light in vacuum, and E_transmitted is the amplitude of the transmitted electric field.
Substituting the expression for the transmitted electric field, we get:
I_transmitted = (1/2)*ε_0*c*(E0*cos(ωt) * cos(θ))^2
= (1/2)*ε_0*c*E0^2*cos^2(ωt) * cos^2(θ)
= (1/2)*ε_0*c*E0^2*cos^2(θ) * (1 + cos(2ωt))/2
= (1/4)*ε_0*c*E0^2*(1 + cos(2ωt))*cos^2(θ)
= (1/4)*ε_0*c*E0^2*cos^2(θ) + (1/4)*ε_0*c*E0^2*cos(2ωt)*cos^2(θ)
The term (1/4)*ε_0*c*E0^2*cos^2(θ) represents the average intensity of the transmitted light, which is given by:
I_avg = (1/4)*ε_0*c*E0^2*cos^2(θ)
So, the average intensity of the transmitted light is proportional to the square of the amplitude of the incident electric field (E0^2) and the square of the cosine of the angle between the incident electric field vector and the x-axis (cos^2(θ)).