Unpolarized light is incident onto three polarizers with their transmission axes oriented in such a way that the first and the last make a 39 angle between them, and the middle one makes the same angle with the first and the last one. Find the percentage of the incident light which passes through these three polarizers.

 I₃ = I₀ 0.395

Explanation:

Polarized light passing through a polarizer must comply with Malus's law

         I = I₀ cos² θ

Before starting, let's analyze the angle between the polarizers, the second has the same angle with the first and the third, so it is at the midpoint

         θ₂ = 39/2 = 19.5

now let's analyze the light that passes through each polarizer, as the incident is unpolarized through the first polarizer half the intensity comes out

          I₁ = I₀ / 2

the second polarizer comes out

          I₂ = I₁ cos² 19.5

          I₂ = I₀ / 2 cos² 19.5

through the third polarized the intensity passes

          I₃ = I₂ cos² 19.5

          I₃ = (I₀ /2 cos² 19.5) cos² 19.5

          I₃ = I₀ 0.395

a charge 3q is at the origin, and a charge −2q is on the positive x axis at x=a. part a where on the x-axis would you place a third charge so it would experience no net electric force? enter an expression for the exact answer, which will involve a square-root sign. (do not enter an approximate decimal answer.)