Answer:
34.24 %
Explanation:
Since I₀ is the intensity of the un-polarized light, the intensity I₁ of the light polarized by the 1st sheet is (by the one-half rule) I₁ = I₀/2.
The intensity of polarized light I from a polarized source I' is I = I'cos²Ф where Ф is the angle between the direction of I' and I. Since the second sheet has its transmission axis at 25° with respect °o the 1st sheet, the intensity of light I₂ from the second sheet is I₂ = I₁cos²25°.
Also, the 3rd sheet has its transmission axis 47° with respect to the 1st sheet. So, the angle between the transmission axis of the 2nd sheet and 3rd sheet is 47° - 25° = 22°. So, the intensity I₃ from the 3rd sheet is I₃ = I₂cos²22°
Finally, the 4th sheet has its transmission axis 10° with respect to the 3rd sheet. So, the intensity I₄ from the 4th sheet is I₄ = I₃cos²10°.
So, I₄ = I₃cos²10°
I₄ = I₂cos²22°cos²10°
I₄ = I₁cos²25°cos²22°cos²10°
I₄ = (I₀/2)cos²25°cos²22°cos²10°
I₄/I₀ = cos²25°cos²22°cos²10°/2
I₄/I₀ = (cos25°cos22°cos10°)²/2
I₄/I₀ = (0.9063 × 0.9272 × 0.9848)²/2
I₄/I₀ = 0.8275²/2
I₄/I₀ = 0.6848/2
I₄/I₀ = 0.3424
So, as a percentage,
I₄/I₀ × 100% = 0.3424 × 100% = 34.24 %
