Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle 3 0 ∘ with each other. What fraction of incident unpolarised light is transmitted? (

Question

Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle 3 0 ∘ with each other. What fraction of incident unpolarised light is transmitted? ( cos 3 0 ∘ = 3 ​ /2 )

TestHub · Accepted Answer

Let the intensity of incident unpolarised light be $I_{0}$ .

When unpolarised light passes through the first polaroid, the intensity of the transmitted polarised light is:

$I_{1} = \frac{I _{0}}{2}$

According to Malus's law, when this polarised light passes through the second polaroid, the transmitted intensity is:

$I_{2} = I_{1} cos^{2} θ$

Given the angle between the transmission axes is $θ = 3 0^{\circ}$ :

$I_{2} = \frac{I _{0}}{2} cos^{2} 3 0^{\circ}$

$I_{2} = \frac{I _{0}}{2} (\frac{3}{2})^{2}$

$I_{2} = \frac{I _{0}}{2} \times \frac{3}{4} = \frac{3}{8} I_{0}$

The fraction of incident light transmitted is:

$\frac{I _{2}}{I _{0}} = \frac{3}{8}$

In percentage, this is:

$\frac{3}{8} \times 100% = 37.5%$

Answer: $37.5%$

Physics - Wave Optics Question with Solution | TestHub

Options:

Doubts & Discussion