Question

Light of intensity I0 passes through 4 ideal polarizing sheets. Unpolarized light enters the 1st sheet that has a horizontal transmission axis. Light continues to the 2nd sheet that has its transmission axis at 25 degrees with respect to the 1st sheet, then to the 3rd sheet that has its transmission axis at 47 degrees with respect to the 1st sheet then to the 4th sheet that has its transmission axis at 10 degrees with respect to the 3d sheet. The intensity of the emerging light as percentage of I0 is close to:

Answer 1

34.24 %

Step-by-step 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 %