Final answer:
The final intensity of transmitted light relative to the intensity of the incident light after passing through seven polarizers oriented at various angles from horizontal to vertical is zero, following Malus's Law for polarized light.
Step-by-step explanation:
The question is asking to calculate the ratio of the final intensity of transmitted light (Ifinal) to the intensity of the incident light (I0) after it passes through seven polarizers, each oriented at different angles with respect to the horizontal.
The angles of the polarizers with respect to the horizontal are 0° (first polarizer), 15°, 30°, 45°, 60°, 75°, and 90° (seventh polarizer).
To solve this, we use Malus's Law, which states that when polarized light passes through a polarizer at an angle θ, the intensity I of the transmitted light is given by I = I0cos2(θ), where I0 is the intensity of the incident polarized light.
The total reduction in intensity is the product of the reduction at each stage. For horizontally polarized light, the initial intensity after the first polarizer remains unchanged, so:
- I1 = I0cos2(15°),
- I2 = I1cos2(15°), since the angle difference between the first and second polarizer is 15°.
- I3 = I2cos2(15°), as each subsequent polarizer is rotated an additional 15° from the previous.
- This process is repeated for each of the seven polarizers.
- I6 = I5cos2(75°), for the angle difference between the sixth and seventh polarizer which is also 15°.
- Finally, the seventh polarizer is vertical, the angle difference with respect to the first polarizer is 90° and the horizontal component is zero, thus I_final = 0.
Therefore, the ratio of I_final/I_0 is 0, as the final polarizer completely blocks the horizontally polarized light.