Question

three polarizing sheets are stacked on top of each other. their polarization directions (relative to an arbitrary reference line) are 0, 45, and 90 degrees. (a) consider the fraction of initially unpolarized incident light that would be transmitted through the stack. does the order in which they are stacked affect your answer? explain briefly. (b) now suppose the first and third sheets are fixed in place, with polarization directions of 0 and 90 degrees respectively; the middle sheet can be rotated. how does the intensity of transmitted light vary qualitatively as you rotate the middle sheet from 0 to 90 degrees?

Answer 1

The intensity of transmitted light through three polarizing sheets is calculated using Malus's Law and is unaffected by the order of stacking. Rotating the middle sheet from 0 to 90 degrees changes the transmitted light intensity from a maximum to zero.

Step-by-step explanation:

For three polarizing sheets stacked with polarization directions at 0, 45, and 90 degrees respectively, the intensity of transmitted light through the stack is affected by Malus's Law, which states that the intensity of light passing through a polarizing filter is proportional to the cosine squared of the angle between the light's initial polarization direction and the axis of the filter. Initially unpolarized light is reduced to 50% after passing through the first polarizer. Subsequently, considering the second polarizer at 45 degrees, the intensity becomes 50% of the remaining light. Finally, the third polarizer at 90 degrees relative to the first would normally block all light, but because of the intermediate polarizer at 45 degrees, some light is transmitted (25% of the remaining intensity).

The order of the polarizing sheets does not affect the final intensity of transmitted light, as the roles of the second and third polarizers in the chain can be interchanged without changing the overall effect. The key factor is the set of relative angles between consecutive polarizers. For part (b), rotating the middle sheet from 0 to 90 degrees would result in a variation of the transmitted light intensity from a maximum (when the middle sheet's axis is aligned with the first sheet) to zero (when the middle sheet's axis is at 90 degrees to both the first and third sheets).