Two polaroids $A$ and $B$ are placed with their polaroid axes $30^{\circ}$ to each other as shown in the figure. A plane polarised light passes through the polaroid $A$ and after passing through it, intensity of light becomes $I_{0}$ . What is the intensity of finally transmitted light after passing through the polaroid $B$ ?

0.75 I_{0}

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0.866 I_{0}

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.025 I_{0}

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0.5 I_{0}

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Solution

The correct option is A $0.75 I_{0}$
Thee intensity $I$ of the transmitted light varies directly as the square of the cosine of the angle between the transmission direction of polariser and analyser
$I = I_{0} {cos}^{2} θ$
Intensity of finally transmitted light after passing through polaroid $B$ is given by $I = I_{0} {cos}^{2} θ$ (Intensity)
$I = I_{0} \cdot {cos}^{2} 30^{\circ}$
$I = I_{0} 0.75$
$I = 0.75 I_{0}$
where, $I_{0}$ is the maximum intensity of transmitted light.

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