Unpolarized light of intensity I passes through polaroid P₁ and then through polaroid P₂ kept at an angle θ with P₁. The intensity of final wave is 

CONCEPT:

• Malus law: This law states that the intensity of the polarized light transmitted through the analyzer varies as the square of the cosine of the angle between the plane of transmission of the analyzer and the plane of the polarizer.

⇒ I = Io cos2θ          

Where Io = Intensity of incoming light and I = Intensity light passing through Polaroid

EXPLANATION:

Combination of polaroids:

• If unpolarized light is passed through two polaroids are placed at an angle θ to each other, the intensity of the polarized wave is

\(⇒ I = \frac{I_o}{2}cos^2θ\)

where I is the intensity of the polarized wave, I₀ is the intensity of the unpolarized wave.

• Therefore option 3 is correct.

Additional Information

• Equation of a transverse wave is given by;

\(⇒ y=Asin(kx-ω t)\)

where A is the amplitude, k the wavenumber, and ω the angular frequency.

Polarization:

• The wave is in the x-y plane, thus it is called a plane-polarized wave.
• The wavefield displaces in the y-direction, thus it is called y-polarized or linearly polarised wave.
• When two orthogonal electric field component vectors are of equal magnitude and are out of phase by exactly 90°, the wave is called circular polarized.

Polaroid:

• A polaroid consists of long-chain molecules aligned in a particular direction.
• The electric vectors along the direction of the aligned molecules get absorbed.
• When an unpolarized light wave is an incident on a polaroid then the light wave gets linearly polarized. 
• This direction of the electric field vector is known as the pass-axis of the polaroid. 

• The intensity of unpolarized light is generally reduced to 50% of the original when passed through a single polaroid.