Two Polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light I₀ is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45º with that of P₁. The intensity of transmitted light through P₂ is

Concept:

Superposition of wave- According to principle of superposition of waves, When two or more waves cross at a point, the displacement at that point is equal to the sum of the displacements of the individual waves. The individual wave displacements may be positive or negative.

There are three effects of superposition of waves:

1 Two waves which have same frequency travel with the same speed along the same direction in a specific medium, then the effect after superposition they  known as the interference of waves.

2. Two waves of same frequencies moving with the same speed along opposite directions in a specific medium, then after superposition they produce stationary waves.

3. Two waves having slightly varying frequencies travelling with same speed along the same direction in a specific medium, then they superpose to produce beats. 

Polaroid: The synthetic plastic sheet used to polarize light is called as Polaroid.

Calculation:

P1 and P2 are placed with their axis perpendicular to each other.

Angle is 90⁰ between P1 and P2 .

Unpolarised light incident on P1 = I0

Angle is 450  between P1 and P3 .

I₂ = \(\frac{l_0}{2}\)cos² 45°

\(=\frac{l_0}{2} \times \frac{1}{2} \)

\(=\frac{l_0}{4}\)

\(l_3 = \frac{l_0}{4}\rm cos^2 \) 45° 

\(l_3 = \frac{l_0}{8}\)