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Malus's law: intensity through polaroids set at given angles to each other

This type of question, asked 4 times: 9 May 2024 S1, 20 Apr 2025 S2, 23 Apr 2025 S1, 13 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    9 May 2024 S1

    19
    A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of emergent light is I0I_0. Now B is rotated by 45∘45^\circ about the ray. The emergent light will have intensity (cos⁡45∘=12\cos45^\circ=\frac{1}{\sqrt{2}})

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  2. Question 2

    20 Apr 2025 S2

    8
    Four polaroid are placed such that the optic axis of each is inclined at an angle of 30∘30^{\circ} the optic axis of the preceding one. If unpolarised light of intensity ' I0I_{0} ' falls on the first polaroid, the intensity of light transmitted from the fourth polaroid is [cos⁡30∘=32]\left\lbrack \cos30^{\circ}=\frac{\sqrt{3}}{2} \right\rbrack

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  3. Question 3

    23 Apr 2025 S1

    47
    Two polaroid are oriented with their planes perpendicular to incident light and transmission axis making an angle 30∘30^{\circ} with each other. What fraction of incident unpolarised light is transmitted?
    (cos⁡30∘=3/2)\left( \cos30^{\circ}=\sqrt{3}/2 \right)

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  4. Question 4

    13 Apr 2026 S2

    142
    'n' polarizing sheets are arranged such that each makes an angle 45∘45^\circ with the preceding sheet. An unpolarized light of intensity II is incident into this arrangement. The output intensity is found to be I/64I/64. The value of nn will be

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