Two Polaroids are placed in the path of an unpolarized beam of intensity I 0 such that no light is emitted from the second polaroid. If a third Polaroid whose polarization axis makes an angle θ with the polarization axis of first Polaroid, is placed between these Polaroids then the intensity of light emerging from the last Polaroid will be

Question

Two Polaroids are placed in the path of an unpolarized beam of intensity I 0 such that no light is emitted from the second polaroid. If a third Polaroid whose polarization axis makes an angle θ with the polarization axis of first Polaroid, is placed between these Polaroids then the intensity of light emerging from the last Polaroid will be, I 0 8 sin 2 2 θ, I 0 4 sin 2 2 θ, I 0 2 cos 4 θ, I 0 cos 4 ⁡ θ

MARKS App · Accepted Answer

If no light comes from 2 nd polaroid, i.e. angle between them = 90 ° If I I I polaroid has polatization axis at angle θ I 2 = I 1 cos 2 ⁡ θ I 2 = I 0 2 cos 2 ⁡ θ As Polarising axis of I & I I are mutually perpendicular Hence angle between polarizing axis of I I & I I I is 90 ° - θ ∴ I 3 = I 2 cos 2 ⁡ 90 ° - θ ⇒ I 3 = I 0 2 cos 2 ⁡ θ sin 2 ⁡ θ ⇒ I 3 = I 0 2 × 4 4 cos 2 ⁡ θ sin 2 ⁡ θ ⇒ I 3 = I 0 8 2 sin ⁡ θ cos ⁡ θ 2 ⇒ I 3 = I 0 8 sin 2 ⁡ 2 θ

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