Final answer:
The fraction of the incident light that passes through P1 is 50%. However, none of the incident light passes through the combination of P1 and P2. With transmission-axis angles of 30.0° and 90.0°, none of the incident light passes through the combination.
Step-by-step explanation:
(a) The fraction of the incident light that passes through P1 can be calculated using Malus' Law, which states that the intensity of light transmitted through a polarizing filter is given by:
I = I0 × cos2(θ)
where I0 is the initial intensity of the incident light and θ is the angle between the polarization axis of the filter and the direction of the incident light. In this case, P1 is at an angle of 45.0° to the beam's axis of polarization. By substituting this angle into the formula, we find that:
I1 = I0 × cos2(45.0°)
I1 = I0 × [cos(45.0°)]2
I1 = I0 × (0.707)2
I1 = I0 × 0.5
Therefore, the fraction of the incident light that passes through P1 is 0.5, or 50%.
(b) The fraction of the incident light that passes through the combination of P1 and P2 can be found by multiplying the fraction of light that passes through each individual filter. Since P2 is at an angle of 90.0° to the beam's axis of polarization, none of the light is transmitted through P2. Therefore, the fraction of the incident light that passes through the combination is 0.5 × 0 = 0.
(c) To calculate the fraction of the incident light that passes through the combination with transmission-axis angles of 30.0° and 90.0° respectively, we can follow the same method as in part (b). Substituting the transmission-axis angles into the formula, we find that:
Fraction of light passed = fraction of light passed through P1 × fraction of light passed through P2
= [cos(30.0°)]2 × [cos(90.0°)]2
= (0.866)2 × 0
= 0
Therefore, with transmission-axis angles of 30.0° and 90.0°, none of the incident light passes through the combination of P1 and P2.