Sunlight scattered from the atmosphere reaches a camera sensor as partially polarized light. At a particular location in the sky, measurements show that 70\% of the incident intensity is polarized along a direction 20∘ above the horizontal; the remaining 30\% is completely unpolarized. A photographer places an ideal linear polarizing filter in front of the camera lens. When the filter’s transmission axis is vertical, it makes an angle of 20∘ with the dominant polarization direction of the partially polarized light.
(a) Define the degree of polarization P of a beam of light and verify that the given sky light has P=0.70.
(b) Derive an expression for the transmitted intensity I(α) as a function of the rotation angle α of the filter’s transmission axis measured from the vertical. Your expression should account for both the polarized and unpolarized components of the incident light.
(c) Using your expression, determine the maximum and minimum transmitted intensities as the photographer rotates the filter through 0∘≤α≤90∘. Express each as a multiple of the total incident intensity I0.
(d) The photographer wants to maximize contrast between the selected region of sky and an unpolarized reference object in the frame. Explain, with quantitative support, how the filter should be oriented to achieve the greatest contrast ratio between the sky region and the reference object’s brightness.