Question

Unpolarized light passes through three polarizing filters. The first one is oriented with a horizontal transmission axis, the second filter has its transmission axis 25.7° from the horizontal, and the third one has a vertical transmission axis. What percent of the light gets through this combination of filters

Answer 1

Answer:

7.6 %

Explanation:

As the first polarizer is oriented with a horizontal transmission axis so the light intensity passes through first polarizer is $I_1=\frac{I_0}{2}$

The second filter has its transmission axis 25.7° from the horizontal so amount if light intensity passes through second polarizer is $I_2=I_1cos^225.27^{\circ}=0.812I_1$  as $I_1=0.5I_0$ so $I_2=0.812\times 0.5I_0=0.406I_0$

Now the third polarizer is has vertical transmission axis so light intensity passes through third polarizer is $I_3=I_2cos^2(90^{\circ}-25.7)=0.188I_2$  as $I_2=0.406I_0$  so  $I_3=0.188\times 0.406I_0=0.076I_0$

$\frac{I_3}{I_0}=\frac{0.076I_0}{I_0}=0.076=7.6$ % so the 7.6 % of the light intensity passes through filter combination

Answer 2

The percentage of light that gets through this combination of filters is 7.7%.

Transmission of light in the first polarizer

From the orientaton of the first polarize with horizontal transmission axis, the light intensity that passes through first polarizer is calculated as;

I₁ = 0.5I₀

Transmission in the second polarizer

The light intensity that passes through second polarizer is calculated as;

I₂ = I₁cos²θ

I₂ = I₁(cos 25.7)²

I₂ = 0.811I₁

I₂ = 0.811(0.5I₀)

I₂ = 0.41I₀

Transmission in the third polarizer

The light intensity that passes through third polarizer is calculated as;

I₃ = I₂cos²(90 - 25.7)

I₃ = 0.188I₂

I₃ = 0.188 x 0.41I₀

I₃ = 0.077I₀

Percentage of light through the filters

I₃/I₀ = 0.077 x 100%

I₃/I₀ = 7.7%

Thus, the percentage of light that gets through this combination of filters is 7.7%.

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