Two polarizer glass are placed at 45 degrees to each other. When a light beam is passed through them ,what percent of the light beam will emerge from the other side. (Options : 100 , 50 ,75 ,25)

Polarizers only involve the electric field vector of the electromagnetic wave. How much gets through the first polarizer depends on the source of the field. If we limit this discussion to visible light from the sun, then the light incident on the first polarizer has all polarizations. The amount passing through the first polarizer is relatively small because the polarizer filters out all light except with a field matching the polarizer’s direction. The question of passing through the second polarizer oriented at 45 deg. to the first one is simple. It is the projection of the E1-vector on the second polarizer.

E2(through the second polarizer) = E1(through the first polarizer) x sin(45 deg)

E2 = E1 x sin(45 deg) =E1 x 1/sqrt(2) = 0.707 E1