Two beams, A and B, of plane polarised light with mutually perpendicular planes of polarisation 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 30° makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IA / IB equals

Question

Two beams, A and B, of plane polarised light with mutually perpendicular planes of polarisation 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 30° makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IA / IB equals (A) 3 (B) 3/2 (C) 1 (D) 1/3

Tardigrade Admin · Accepted Answer

By law of Malus, I=I0 cos 2 θ Now, IA prime=IA cos 2 30 IB'=IB cos 2 60 As IA'=IB' ⇒ IA × (3/4)=IB × (1/4) (IA/IB)=(1/3)

3

3/2

1

1/3

By law of Malus, I=I0​cos2θ Now, IA′​=IA​cos230 IB′​=IB​cos260 As IA′​=IB′​ ⇒IA​×43​=IB​×41​ IB​IA​​=31​

By law of Malus, $I = I_{0} cos^{2} θ$
Now, $I_{A^{'}} = I_{A} cos^{2} 30$
$I_{B^{'}} = I_{B} cos^{2} 60$
As $I_{A^{'}} = I_{B^{'}}$
$\Rightarrow I_{A} \times \frac{3}{4} = I_{B} \times \frac{1}{4}$
$\frac{I _{A}}{I _{B}} = \frac{1}{3}$