Physics Problem: Angle of a Polarizing Filter
Question:
What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity 1.00 kW/m² to reduce the intensity to 500 W/m²?
- 40.0 degrees
- 450 degrees
- 50.0 degrees
- 35.0 degrees
Answer:
To solve this, we apply Malus’s Law, which describes how the intensity of polarized light changes after passing through a polarizing filter.
I = I0 × cos²(θ)
Where:
- I0 = initial intensity of the light = 1.00 kW/m² = 1000 W/m²
- I = final transmitted intensity = 500 W/m²
- θ = angle between the light’s polarization direction and the filter’s axis
Step-by-Step Calculation:
Using Malus’s Law:
500 = 1000 × cos²(θ)
Divide both sides by 1000:
cos²(θ) = 500 / 1000 = 0.5
Take the square root of both sides:
cos(θ) = √0.5 ≈ 0.7071
Now, take the inverse cosine:
θ = cos⁻¹(0.7071) ≈ 45.0°
Final Answer:
The axis of the polarizing filter must be oriented at an angle of 45.0° relative to the polarization direction of the incident light.
Correct Option:
45.0 degrees (Note: The “450 degrees” in the options is likely a typographical error for “45.0 degrees”)