The ratio of the intensity between light intensity that emerges from the last filter and unpolarized light of intensity, I₀ is It/I₀ = 0.2925
To answer the question, we need to know what polarization of light is.
<h3>What is polarization of light?</h3>
This is when the electric field vector of light is oscillating in one plane.
- Now for light of intensity I' which is initially unpolarized, its intensity after polarization is I = 1/2I'.
- Also, for light initially polarized, its intensity after polarization is I"' = I"cos²Ф where Ф is the angle between the initial direction and the direction of polarization.
<h3>Intensity of light through each polarized filter</h3>
Given that we have 7 polarizing filters, each rotated 17° cw with respect to the previous filter.
So, since the light is initially unpolarized,
- The intensity through the first polarizing filter is I₁ = 1/2I₀ where I₀ is the initial intensity.
- The intensity through the second polarizing filter is I₂ = I₁cos²17°= 1/2I₀cos²17°
- The intensity through the third polarizing filter is I₃ = I₂cos²17° = 1/2I₀cos⁴17°
- The intensity through the fourth polarizing filter is I₄ = I₃cos²17° = 1/2I₀cos⁶17°
- The intensity through the fifth polarizing filter is I₅ = I₄cos²17° = 1/2I₀cos⁸17°
- The intensity through the sixth polarizing filter is I₆ = I₅cos²17° = 1/2I₀cos¹⁰17°
- The intensity through the seventh polarizing filter is I₇ = I₆cos²17° = 1/2I₀cos¹²17°.
<h3>The ratio of the intensity between light intensity that emerges from the last filter and unpolarized light of intensity</h3>
Since I₇ is the last intensity I₇ = It = 1/2I₀cos¹²17°.
So, It/I₀ = 1/2cos¹²17°
= 1/2(0.9563)¹²
= 1/2 × 0.5850
= 0.2925
So, the ratio of the intensity between light intensity that emerges from the last filter and unpolarized light of intensity, I₀ is It/I₀ = 0.2925
Learn more about intensity of polarized light here:
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