JEE Main · 2014 · 06 Apr 2014 · Offline · Wave Optics

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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

3 0^{0}

makes the two beams appear equally bright. If the initial intensities of the two beams are

I_{A}

and

I_{B}

respectively, then

I_{A} / I_{B}

equals:

(A)1
(B) $1/3$ ✓ Correct
(C)3
(D) $3/2$

Answer: (B)

Solution

Work with Malus's law from the starting position, where

A

is fully passed and

B

fully blocked. Turning the polaroid by

3 0^{\circ}

makes

A

's plane

3 0^{\circ}

from the axis and

B

's plane

6 0^{\circ}

from it. The transmitted intensities are

I_{A} cos^{2} 3 0^{\circ}

and

I_{B} cos^{2} 6 0^{\circ}

, and these are now equal, so

I_{A} cos^{2} 3 0^{\circ} = I_{B} cos^{2} 6 0^{\circ}

. Hence

\frac{I _{A}}{I _{B}} = \frac{cos ^{2} 6 0 ^{\circ}}{cos ^{2} 3 0 ^{\circ}} = \frac{1/4}{3/4} = \frac{1}{3}

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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JEE Main · 2014 · 06 Apr 2014 · Offline · Wave Optics

Solution

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