Unpolarized light of intensity I₀ is made to pass through three polarizers P₁ , P₂ and P₃ successively. The polarization axis of P₂ makes an angle of 60^ with that of P₁ , while that of P₃ makes an angle of 45^ with that of the P₂ . If I₀ = xI₃ , the value of ' x ' is ( 45^ = 1 2 , 60^ = 1 2 )

Step-by-step solution

Intensity of unpolarized light is I₀ . Intensity of light after passing through the first polarizer P₁ is: I₁ = I₀ 2 The polarization axis of P₂ makes an angle of 60^ with P₁ . According to Malus's law, the intensity after passing through P₂ is: I₂ = I₁ ^2(60^ ) = I₀ 2 ( 1 2 )^2 = I₀ 8 The polarization axis of P₃ makes an angle of 45^ with P₂ . The intensity after passing through P₃ is: I₃ = I₂ ^2(45^ ) = I₀ 8 ( 1 2 )^2 = I₀ 16 Given I₀ = x I₃ , substituting the value of I₃ gives: I₀ = x ( I₀ 16 ) x = 16 Answer: 16