What happens to the intensity of light when it passes through two polarizers at an angle of 45 degrees?

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Q: What happens to the intensity of light when it passes through two polarizers at an angle of 45 degrees?

Solution: The intensity of light passing through two polarizers at an angle of 45 degrees is quartered.

Steps: 9

Step 1: Start with unpolarized light. This light has waves vibrating in all directions.
Step 2: The first polarizer only allows light waves that are aligned with its direction to pass through. This reduces the intensity of the light to half of its original value.
Step 3: Now, the light that comes out of the first polarizer is polarized in one direction.
Step 4: The second polarizer is at a 45-degree angle to the first one. It will allow some of the polarized light from the first polarizer to pass through.
Step 5: To find the intensity of light after the second polarizer, use Malus's Law, which states that the intensity of light passing through a polarizer is equal to the intensity of the incoming light times the cosine squared of the angle between the light's polarization direction and the polarizer's direction.
Step 6: The angle between the first and second polarizer is 45 degrees. The cosine of 45 degrees is 0.707 (approximately).
Step 7: Calculate the intensity after the second polarizer: I = I1 * (cos(45 degrees))^2. Since I1 is half of the original intensity, we have I = (0.5 * I0) * (0.707)^2.
Step 8: (0.707)^2 is approximately 0.5, so I = (0.5 * I0) * 0.5 = 0.25 * I0.
Step 9: This means the intensity of light after passing through both polarizers is one quarter of the original intensity.