Q175 / 180 · COMEDK 2012 · Physics

Two polaroid $A$ and $B$ are kept with their transmission axes at an angle $\theta$ with respect to one another. If the transmitted intensity of light $I_{t}=0.75 I_{0}$, where $I_{0}$ is the intensity of light incident on the system, then $\theta$ is
Figure

  • Correct answer
    A
    $30^{\circ}$
  • B
    $45^{\circ}$
  • C
    $60^{\circ}$
  • D
    $90^{\circ}$

Solution

For two polaroids placed at an axis making angle $\theta$ with each other, then according to law of malus, the intensity of transmitted light is Here, $$ \begin{aligned} &I_{t}=I_{0} \cos ^{2} \theta \\ &I_{t}=0.75 I_{0} \end{aligned} $$ $\Rightarrow \quad 0.75 I_{0}=I_{0} \cos ^{2} \theta$ $\Rightarrow \quad \cos ^{2} \theta=0.75=\frac{3}{4}$ $\Rightarrow \quad \theta=\cos ^{-1} \sqrt{\frac{3}{4}}=\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ $\therefore \quad \theta=30^{\circ}$

Hence, the correct answer is option: 'A'.

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