Polarization through Three Polarisers – Rankers Physics

Miscellaneous: Practice Problem & Solution

Assertion (A): If three polarisers are arranged such that the axis of any two successive polarisers make equal angle with each other. If unpolarised light of intensity \(I_0\) incident on first polariser then intensity of emergent light after 3rd polariser is \(\frac{I_0}{8}\). If angle between them is \(45^\circ\). Reason (R): Each time intensity becomes \(50%\) by Malus law.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Miscellaneous. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. Intensity after 1st polariser is \(I_1 = I_0/2\). Given angle between successive polarisers is \(\theta = 45^\circ\). By Malus' Law, \(I_2 = I_1 \cos^2(45^\circ) = (I_0/2)(1/2) = I_0/4\). \(I_3 = I_2 \cos^2(45^\circ) = (I_0/4)(1/2) = I_0/8\). Reason (R) is false. Intensity becomes 50% only when \(cos^2\theta = 0.5\) (i.e., \(\theta = 45^\circ\)) and only for polarized light. The first polarizer reduces unpolarized light to 50% without \(cos^2\theta\) dependence. So, the general statement 'each time intensity becomes 50%' is false.

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