Question

The intensity of a polarized electromagnetic wave is 10 w/m2. What will be the intensity after passing through a polarizing filter whose axis makes the following angles with the plane of polarization? (a) u = 0°, (b) u = 30°, (c) u = 45°, (d) u = 60°, (e) u = 90°.

Answer 1

Using Malus's Law, the intensity of a polarized wave after passing through a polarizing filter depends on the angle between the filter axis and the wave's polarization. The initial intensity of 10 w/m2 changes at different angles, with complete transmission at 0° and complete blockage at 90°.

Step-by-step explanation:

The student has asked about the change in intensity of a polarized electromagnetic wave after it passes through a polarizing filter at various angles. This scenario can be described using Malus's Law, which states that the intensity of the transmitted wave (I) is equal to the initial intensity (I0) times the square of the cosine of the angle (θ) between the original polarization direction and the filter axis:

I = I0 × cos²(θ)

Given that the initial intensity is 10 w/m2, the transmitted intensities at different angles are:

• (a) u = 0°: I = 10 × cos²(0°) = 10 w/m2 (No change)
• (b) u = 30°: I = 10 × cos²(30°) = 10 × (0.866²) ≈ 7.50 w/m2
• (c) u = 45°: I = 10 × cos²(45°) = 10 × (0.707²) = 5 w/m2
• (d) u = 60°: I = 10 × cos²(60°) = 10 × (0.5²) = 2.50 w/m2
• (e) u = 90°: I = 10 × cos²(90°) = 0 w/m2 (Completely blocked)