An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90° , respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.

Step-by-step solution

Let the intensity of the incident unpolarized light be I₀ . After passing through the first polarizer, the intensity becomes I₁ = I₀ 2 . Without the third polarizer, the light passes directly from the first polarizer (at 30^ ) to the second polarizer (at 90^ ). The angle between their transmission axes is 90^ - 30^ = 60^ . Using Malus's law, the output intensity without the third polarizer is: I_ without = I₁ ^2(60^ ) = I₀ 2 ( 1 2 )^2 = I₀ 8 When the third polarizer (at 60^ ) is placed between them, the light first