Two ideal polarizing filters are oriented so that they transmit the maximum amou

Question

Two ideal polarizing filters are oriented so that they transmit the maximum amount of light when unpolarized light is shone on them.

A) To what fraction of its maximum value is the intensity of the transmitted light reduced when the second filter is rotated through 22.0 degrees ?
Enter the fraction only.

B) To what fraction of its maximum value is the intensity of the transmitted light reduced when the second filter is rotated through 42.5 degrees ?
Enter the fraction only.

C) To what fraction of its maximum value is the intensity of the transmitted light reduced when the second filter is rotated through 68.0 degrees?
Enter the fraction only.

Explanation / Answer

Using Malus' law, intensity of light coming out of the second filter is given by I=I_0 cos^2 y, where I_0 is the intensity of light coming out of first filter( i.e. maximum amount of light incident on second filter) So fraction of maximum value transmitted is I/I_0 = cos^2 y and intensity is reduced by fraction of 1 - I/I_0 A] Fraction of light transmitted = cos^2 22deg = 0.8596 or 85.96% Intensity is reduced by fraction of 1-0.859 = 0.14.1 or 14.1% B] Fraction of light transmitted= cos^2 45deg = 0.5435 or 54.35% Intensity is reduced by fraction of 1-0.5435 = 0.4565 or 45.65% C] Fraction of light transmitted= cos^2 65.5deg = 0.14 or 14% Intensity is reduced by fraction of 1-0.11 = 0.859 or 85.9%

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