Unpolarized light of intensity I₀ passes through four polaroids arranged in series. The transmission axis of each subsequent polaroid is rotated by an angle of 30^ relative to the preceding one. What is the final transmitted intensity of light through the fourth polaroid?

Step-by-step solution

When unpolarized light of intensity I₀ passes through the first polaroid, its intensity is halved: I₁ = I₀ 2 The light then passes through the second polaroid, whose axis is at 30^ to the first. According to Malus's Law: I₂ = I₁ ^2(30^ ) = I₀ 2 ( 3 2 )^2 = I₀ 2 3 4 The third polaroid is at 30^ to the second: I₃ = I₂ ^2(30^ ) = ( I₀ 2 3 4 ) 3 4 = I₀ 2 ( 3 4 )^2 The fourth polaroid is at 30^ to the third: I₄ = I₃ ^2(30^ ) = I₀ 2 ( 3 4 )^2 3 4 = I₀ 2 ( 3 4 )^3 Calculating the final value: I₄ = I₀ 2 27 64 = 27 I₀ 128 A