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 t

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

TestHub · 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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