The following are positioned in sequence: A source of beam of natural light intensity I0; three ideal polarizers A, B, C; and an observer. Polarizer axis angles are measured clockwise from the vertical, from the perspective of the observer. The axis of polarizer A is set a zero degrees (vertical), and the axis angle of polarizer C is set at 50 degrees.A) If polarizer B is set so the beam intesity is zero at the observer, what are the two possible axis angle settings of polarizer B?B) If polarizer B is set so that the beam intensity at the observer is a maximum, what is the axis angle of the polarizer B? Please show detailed stepsC) If the axis angle of polarizer B is set to 120degrees, what is the ratio of the intensity of the beam at the observer to the intensity of the source?

The intensity transmitted by a polarizer is maximum in the direction of polarization axis and zero in the direction perpendicular to this axis, for the arbitrary direction the intensity transmitted is governed by the expression

I = I₀ cos² θ

A) Let's analyze the situation if the polarizer A is in the vertical direction all the transmitted light has vertical polarization. There are two possibilities of placing polarizer B

• Polarizer B may be perpendicular to bony polarizer A in the horizontal direction so that the transmitted light is zero.

• The polarizer B can be perpendicular to the polarizer C bone 90 ±50º = 140º or 40º respect to the vertical and the light will also be zero

B) For maximum transmission, polarizers B and C must be parallel, this implies that polarizer B is 50º from vertical or polarizer B is parallel to polarizer A

Case 1. Parallel A and B I₁ = I₀

B and C at 50º I₂ = I₀ cos² 50

Case 2 A and B at 50º I₁ = I₀ cos² 50

Parallel B and C I₂ = I₁1

I₂ = I₀ cos² 50

C) For this part we use the initial intensity equation for each pair of polarizers

Between polarizers A and B

I₁ = I₀ cos² 120

I₁ = I₀ 0.25

Let's look at the angle between polarizers B and C

θ = 120-50

θ = 70º

I₂ = I₁ cos² 70

I₂ = 0.25 Io 0.1169

I₂ = 0.029 I₀

The final intensity is

I₂ / I₀ = 0.029