Wave Optics

JEE Main level, single correct, medium

186 of 191

Question 186 of 191

Two beams, A and B of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of polaroid through 30o makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IAIB\dfrac{{\text{I}}_{\text{A}}}{{\text{I}}_{\text{B}}} equals :

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Answer: (D) 13\dfrac{1}{3}

IAcos2θ=IBcos2(90−θ){\text{I}}_{\text{A}}{\text{cos}}^{2}\theta ={\text{I}}_{\text{B}}{\text{cos}}^{2}\left(90-\theta \right) (I=I0cos2θ)\left(\text{I}={\text{I}}_{0}{\text{cos}}^{2}\theta \right) by malus equation

∴IAIB=tan2θ=13∴\dfrac{{\text{I}}_{\text{A}}}{{\text{I}}_{\text{B}}}={\text{tan}}^{2}\theta =\dfrac{1}{3}

where θ=30o\theta =3{0}^{\text{o}}

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