Question

Consider 3 polarizers. Polarizer 1 has a vertical transmission axis and polarizer 3 has a horizontal transmission axis. Taken together, polarizers 1 and 3 are a pair of crossed polarizers. Polarizer 2, with a transmission axis of 30o to the vertical, is placed between polarizers 1 and 3. What is the intensity of light transmission that these polarizers given an initial intest of light Io?

A. 0.375 Io
B. 0.25 Io
C. 0.18 Io
D. 0.09 Io
E. zero

Answer 1

Answer:

Option D.) 0.09 I₀

Explanation:

The intensity, I, of a polarized light after passing through a polarizing filter is given by $I = I_{0} cos^{2} \theta$

$I_{0} =$ Original Intensity

$\theta =$ Angle between the direction of polarization and the axis of filter

After passing through the first polarizer, the initial intensity, $I_{o}$ is halved, i.e $I_{1} = \frac{I_{0} }{2}$

After passing through the second polarizer, the angle of polarization, θ = 30⁰

$I_{2} = I_{1} cos^{2} \theta$

$I_{2} = \frac{I_{0} }{2} cos^{2} 30\\I_{2} =\frac{3}{8} I_{0} \\I_{2} = 0.375 I_{0}$

After passing through the third polarizer, the angle of polarization, θ = 90⁰-30⁰ = 60⁰

$I_{3} = I_{2} cos^{2} \theta$

$I_{3} = 0.375I_{0} cos^{2} 60$

$I_{2} =0.09 I_{0}$