Final answer:
The intensity of the transmitted light after passing through the polarizing filter with an angle of 40° is approximately 0.18 W/m².
Step-by-step explanation:
To find the intensity of the transmitted light after passing through a polarizing filter with an angle of 40°, we first need to calculate the angle between the polarization direction of the incident light and the transmission axis of the filter. Since the transmission axis of the filter is at an angle of 40° with the vertical, and the vertical is at an angle of 90° with the polarization direction, we can subtract the two angles to get the relative angle between the polarization direction and the transmission axis, which is 90° - 40° = 50°.
Next, we can use the formula I = I₀cos²θ, where I is the intensity of the transmitted light, I₀ is the intensity of the incident light (0.45 W/m²), and θ is the angle between the polarization direction and the transmission axis (50°).
Substituting the values into the formula, we get I = 0.45 W/m² * (cos50°)² = 0.45 W/m² * (0.6428)² ≈ 0.18 W/m².