Final answer:
When two polarizing sheets are placed together with their transmission axes at an angle θ, the intensity of transmitted light can be calculated using Malus' Law. When only 25% of the maximum transmitted light intensity passes through the sheets, the angle θ is ±45°.
Step-by-step explanation:
When two polarizing sheets P₁ and P₂ are placed together with their transmission axes oriented at an angle θ to each other, the intensity of the transmitted light can be calculated using Malus' Law. Malus' Law states that the intensity of the transmitted light is equal to the initial intensity of the light multiplied by the square of the cosine of the angle between the transmission axis of the two sheets.
Using this equation, we can solve for θ when only 25% of the maximum transmitted light intensity passes through the sheets:
0.25 = cos²(θ)
Taking the square root of both sides of the equation:
√(0.25) = cos(θ)
Therefore, θ = ± 45°.