Afilm of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. if it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths

Unpolarized light falls on two polarizer sheets whose transmission axes are at right angles. a third polarizer is placed between the first two so that its axis makes a 52-degree angle with the axis of the first polarizer. a) what fraction of the incident light intensity is transmitted through the first polaroid? b) what fraction of the incident light intensity is transmitted through the second polaroid? c) what is the angle of polarization of the light that enters the third polaroid? d) what fraction of the incident light intensity is transmitted through the third polaroid. e) what happens if the middle polaroid is removed?