Linearly polarized light is incident on a piece of polarizing material. What is the ratio of the transmitted light intensity to the incident light intensity when the angle between the transmission axis and the incident electric field is (a) 30° and (b) 71°?

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Polarized light is incident on a sheet of polarizing material and only 22% of the light gets through. Find the angle between the electric field and the transmission axis

To calculate the ratio of transmitted light intensity to incident light intensity, we can use Malus' law. According to Malus' law, the ratio of the transmitted intensity (I_t) to the incident intensity (I_i) is given by:

I_t / I_i = cos^2(θ)

where θ is the angle between the transmission axis and the incident electric field.

(a) When θ = 30°:
I_t / I_i = cos^2(30°) = 0.75

Therefore, the ratio of transmitted light intensity to incident light intensity is 0.75 when the angle between the transmission axis and the incident electric field is 30°.

(b) When θ = 71°:
I_t / I_i = cos^2(71°) = 0.047

Therefore, the ratio of transmitted light intensity to incident light intensity is 0.047 when the angle between the transmission axis and the incident electric field is 71°.

I can definitely help you with that! To find the ratio of the transmitted light intensity to the incident light intensity, we need to consider Malus's Law. According to Malus's Law, the intensity of the transmitted light through a polarizing material is given by the equation:

I_t = I_0 * cos^2(theta)

Where:
- I_t represents the transmitted light intensity,
- I_0 represents the incident light intensity, and
- theta represents the angle between the transmission axis and the incident electric field.

Let's calculate the ratio of transmitted light intensity to incident light intensity for the given angles:

(a) When the angle theta is 30°:
- Plug in the value of theta into the equation: I_t = I_0 * cos^2(30°)
- Calculate the cosine of 30°: cos(30°) = sqrt(3) / 2
- Substitute the value: I_t = I_0 * (sqrt(3)/2)^2 = I_0 * 3/4 = 3I_0 / 4
- The ratio of transmitted to incident light intensity is 3/4 or 0.75.

(b) When the angle theta is 71°:
- Plug in the value of theta into the equation: I_t = I_0 * cos^2(71°)
- Calculate the cosine of 71°: cos(71°) ≈ 0.327
- Substitute the value: I_t = I_0 * (0.327)^2 ≈ I_0 * 0.107 = 0.107I_0
- The ratio of transmitted to incident light intensity is approximately 0.107.

So, for (a) 30°, the ratio is 0.75, and for (b) 71°, the ratio is approximately 0.107.