Polarization

Step 1: Understanding the Concept:
This problem involves Malus's Law, which describes the intensity of light transmitted through a series of polarizers. We have three polarizers: a first polarizer (P1), a middle polaroid sheet (P2), and a third polarizer (P3) which is crossed with the first.

Step 2: Key Formula or Approach:
Malus's Law states that if the angle between the transmission axes of two polarizers is , the intensity of the transmitted light is related to the incident polarized light intensity by: Let's denote the angles of the transmission axes of P1, P2, and P3 with respect to some reference (e.g., the vertical) as .

Step 3: Detailed Explanation:
Let the initial unpolarized light have intensity . The first polarizer (P1) polarizes the light, and its transmitted intensity is . Let's set the axis of P1 to be at . The third polarizer (P3) is "crossed" with the first one. This means their axes are perpendicular. So, (or 90°). The middle polaroid sheet (P2) is rotated. Let its axis be at an angle with respect to the first polarizer's axis. So, . Now, let's trace the intensity: 1. Intensity after P1: . 2. Intensity after P2: The light incident on P2 has intensity and is polarized at angle 0. The angle between P1 and P2 is . Using Malus's Law: 3. Intensity after P3: The light incident on P3 has intensity and is polarized at angle . The axis of P3 is at . The angle between P2 and P3 is . Using Malus's Law again: Substituting the expression for : We want to find the angle that maximizes this final intensity . We can use the trigonometric identity . The intensity will be maximum when is maximum. The maximum value of is 1. This occurs when: The angle given in the options is .

Step 4: Final Answer:
The transmitted intensity is maximum when the angle between the first polarizer and the middle polaroid is .