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Three ideal polaroids P₁ , P₂ , and P₃ are arranged coaxially. The transmission axes of P₁ and P₃ are perpendicular to each other. The polaroid P₂ is placed between P₁ and P₃ such that its transmission axis makes an angle of 30^ with that of P₁ . If an unpolarised light beam of intensity I₀ is incident on P₁ , the intensity of the light emerging from P₃ will be :

Options

  1. A3I₀ 16
  2. B9I₀ 32
  3. C0
  4. D3I₀ 32

Correct answer

D. 3I₀ 32

Step-by-step solution

When unpolarised light of intensity I₀ passes through the first polaroid P₁ , its intensity is halved. Intensity after P₁ , I₁ = I₀ 2 The light is now plane-polarised parallel to the axis of P₁ . It then passes through P₂ , whose axis is at an angle of 30^ to that of P₁ . By Malus's law: Intensity after P₂ , I₂ = I₁ ^2(30^ ) = I₀ 2 ( 3 2 )^2 = 3I₀ 8 The transmission axes of P₁ and P₃ are perpendicular (angle is 90^ ). Since P₂ is at 30^ to P₁ , the angle between the axes of P₂ and P₃ is 90^ - 30^ = 60^ . Applying M

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