Question

light known to be polarized in the horizontal direction is incident on a polarizing sheet. it is observed that only 15.0% of the intensity of the incident light is transmitted through the sheet. what angle does the transmission axis of the sheet make with the horizontal?

Answer 1

The transmission axis of the sheet makes an angle of approximately 67° with the horizontal.

The intensity transmitted through a polarizing sheet is given by Malus's Law, which states that the transmitted intensity
`\(I_t\)` is related to the incident intensity
`\(I_0\)` and the square of the cosine of the angle (θ) between the transmission axis and the direction of polarization:

`\[ I_t = I_0 \cdot \cos^2(\theta) \]`

Given that only 15.0% of the intensity is transmitted, we can express this as:

`\[ I_t = 0.15 \cdot I_0 \]`

`\[ 0.15 \cdot I_0 = I_0 \cdot \cos^2(\theta) \]`

`\[ 0.15 = \cos^2(\theta) \]`

`\[ \theta = \cos^(-1)\left(√(0.15)\right) \]` = 67° (approximate)

The angle of transmission with the horizontal is approximately 67°.

Answer 2

We can see here that the angle the transmission axis of the sheet makes with the horizontal is approximately 67°

The angle that the transmission axis of the polarizing sheet makes with the horizontal can be determined using the concept of Malus' Law.

According to Malus' Law, the intensity of light transmitted through a polarizing sheet is given by the equation:

I = I₀ × cos²(θ)

Where:

• I is the intensity of the transmitted light,

• I₀ is the intensity of the incident light, and

• θ is the angle between the transmission axis of the sheet and the direction of polarization of the incident light.

In this case, we know that only 15.0% of the intensity of the incident light is transmitted through the sheet. Therefore, we can rewrite the equation as:

0.15 × I₀ = I₀ × cos²(θ)

Simplifying the equation, we have:

0.15 = cos²(θ)

To find θ, we need to take the square root of both sides of the equation:

cos(θ) = √0.15

Taking the inverse cosine (cos⁻¹) of both sides, we can find θ:

θ = cos⁻¹(√0.15) = cos⁻¹ 0.387298335

= 67.213°.

Thus, the angle the transmission axis of the sheet makes with the horizontal is approximately 67°.