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Wave Optics

Section: Physics

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Question : 4 of 13

Marks: +1, -0

An unpolarised beam of light incidents on a group of three polarising sheets arranged such that the angle between the axes of any two adjascent sheets is

30^{\circ}

. The ratio of the intensities of polarised light emerging from the second and third sheets is

[AP EAPCET 22 May 2025 S1]

$1:1$
$2:1$
$4:3$
$3:2$

Solution:

When unpolarised light of intensity

(I_0)

passes through the first polariser, the intensity reduces to half

\left(\;\frac{I_0}{2}\right)

.

According to law of Malus, intensity after second polariser.

I_2=\;\frac{I_0}{2}\cos^2 30^{\circ}=\;\frac{I_0}{2}\times\;\frac{3}{4}=\;\frac{3 I_0}{8}

The angle between the second and third polariser is also

30^{\circ}

. The intensity after the third polariser

\;I_3=I_2\cos^2 30^{\circ}

\;=\;\frac{3 I_0}{8}\times\;\frac{3}{4}=\;\frac{9 I_0}{32}

\therefore \;\; \frac{I_2}{I_3} = \;\frac{\;\frac{3 I_0}{8}}{\frac{9 I_0}{32}} = \;\frac{4}{3}

\therefore \; I_2 : I_3 = 4 : 3

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