Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 98% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes through the second sheet. What angle does the transmission axis of the second sheet make with the vertical? (Let the +y-axis represent the upward vertical direction. Express your answer as a value between 0° and 180°.)
To find the angle at which the transmission axis of the second sheet makes with the vertical, we can use Malus's law. Malus's law states that the intensity of light transmitted through a polarizer is given by the equation:
I = I₀ * cos²(θ)
Where I is the intensity of the transmitted light, I₀ is the initial intensity of the incident light, and θ is the angle between the transmission axis of the polarizer and the polarization direction of the incident light.
Given that only 98% of the intensity of the light passes through the first sheet of the polarizing material, we can express this as:
I / I₀ = 0.98
Using Malus's law, we substitute this value into the equation:
0.98 = cos²(θ)
To find the angle θ, we can take the square root of both sides of the equation:
cos(θ) = √0.98
Taking the inverse cosine (arccos) of both sides gives us the value of θ:
θ = arccos(√0.98)
Now, we can solve for θ using a calculator. By evaluating arccos(√0.98), we find that:
θ ≈ 11.543°
Since we are asked to express the answer as a value between 0° and 180°, we can conclude that the transmission axis of the second sheet makes an angle of approximately 11.543° with the vertical.