A stack of n ideal polarizers is arranged so that the transmiss ion axes of the

Question

A stack of n ideal polarizers is arranged so that the transmiss ion axes of the first and last polarizers are perpendicular to each other. The remaining polariz ers are oriented so that there are equal angles bet ween any two successive polarizers (giving a net rotation of 90 for light passing all the way through the stack.

(a) Suppose that light polarized parallel to the tr ansmission axis of the first polarizer, with intens ity I 0 is incident on the stack. What is the intensity of the outgoing l ight? (Find a general formula in terms of n .)

A stack of n ideal polarizers is arranged so that the transmiss ion axes of the first and last polarizers are perpendicular to each other. The remaining polariz ers are oriented so that there are equal angles bet ween any two successive polarizers (giving a net rotation of 90½ for light passing all the way through the stack. (a) Suppose that light polarized parallel to the tr ansmission axis of the first polarizer, with intens ity I 0 is incident on the stack. What is the intensity of the outgoing l ight? (Find a general formula in terms of n .) (b) Show that in the limit n -- > Infinity your answer from (a) becomes I 0 . (Hint: Rather than trying to directly evaluate the limit of your result from (a), evaluat e the logarithm of this expression. Find an expression to which you can apply l'Hopital's rule.)

Explanation / Answer

apply malus law as I = Io cos^2 theta

after passing through first polarizer, I falls by Io/2

so

when theta   = 0 deg

cos theta = cos 0 = 1

so

I = io/2 * cos^2(1)

I = io/2

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