Question

In the Figure, a beam of light, with intensity 43 W/m² and polarization parallel to a y axis, is sent into a system of two polarizing sheets with polarizing directions at angles of θ₁ = 70^o and θ₂ = 90^o to the y axis. What is the intensity of the light transmitted by the two-sheet system?

Answer 1

We know, according to Malus law, if a beam of light having intensity I_o passes through a polarizer, which has its polarization axis at an angle with the direction of the polarization of the incident beam, then the intensity of the transmitted beam becomes equal to I = I_o cos².

Here, I_o = 43 W / m².

Thus, the beam transmitted from the first polarizing sheet is : I₁ = I_o cos²₁,

and, the beam transmitted from the first polarizing sheet is : I₂ = I₁ cos² ( ₂ - ₁ ),

or, I₂ = I_o x cos²₁ x cos² ( ₂ - ₁ ).

Putting values,

I₂ = 43 W / m² x cos² 70^o x cos² ( 90 - 70 )^o

Hence, I₂ ~ 4.44 W / m².

Thus,  the intensity of the light transmitted by the two-sheet system is : 4.44 W / m².