Unpolarized light from an incandescent lamp has an intensity 112.0 Cd as measured by a light meter.

a) What is in Cd the intensity reading on the meter when a single ideal polarizer is inserted between the bulb and the meter?

b) What is in Cd the intensity reading on the meter when two ideal polarizers are inserted between the bulb and the meter with their axis of polarization aligned?

c) What is in Cd the intensity reading on the meter when two ideal polarizers are inserted between the bulb and the meter with their axis of polarization making an angle of 45° relative to each other?

d) What is in Cd the intensity reading on the meter when two ideal polarizers are inserted between the bulb and the meter with their axis of polarization making an angle of 90° relative to each other?

e) What is in Cd the intensity reading on the meter when two ideal polarizers are inserted between the bulb and the meter with their axis of polarization making an angle of θ = 4.0° relative to each other?

a) When a single ideal polarizer is inserted between the bulb and the meter, the intensity reading on the meter is given by Malus' Law, which states that the intensity transmitted through a polarizer is equal to the initial intensity multiplied by the cosine squared of the angle between the transmission axis of the polarizer and the initial direction of polarization.

In this case, with an unpolarized light source, the initial intensity is 112.0 Cd. Since the single polarizer is inserted, the transmitted intensity can be calculated as follows:

Transmitted intensity = Initial intensity * (cos(angle))^2

Since there is only one polarizer, the angle between the transmission axis and the initial direction of polarization is 90 degrees (perpendicular). Therefore:

Transmitted intensity = 112.0 Cd * (cos(90))^2
Transmitted intensity = 0 Cd (Since the transmitted intensity is zero when the angle is perpendicular to the initial direction of polarization)

So, the intensity reading on the meter with a single ideal polarizer is 0 Cd.

b) When two ideal polarizers are inserted between the bulb and the meter, with their axis of polarization aligned, the transmitted intensity is given by the same Malus' Law as before. The initial intensity is 112.0 Cd, and since the transmission axes of both polarizers are aligned, the angle between them is 0 degrees. Therefore:

Transmitted intensity = Initial intensity * (cos(0))^2
Transmitted intensity = 112.0 Cd * (1)^2
Transmitted intensity = 112.0 Cd

So, the intensity reading on the meter with two ideal polarizers aligned is 112.0 Cd.

c) When two ideal polarizers are inserted between the bulb and the meter, with their axis of polarization making an angle of 45 degrees relative to each other, the transmitted intensity can be calculated using Malus' Law. The initial intensity is 112.0 Cd, and the angle between the transmission axes of the polarizers is 45 degrees. Therefore:

Transmitted intensity = Initial intensity * (cos(45))^2
Transmitted intensity = 112.0 Cd * (0.707)^2
Transmitted intensity ≈ 79.24 Cd (rounded to two decimal places)

So, the intensity reading on the meter with two ideal polarizers at a 45-degree angle is approximately 79.24 Cd.

d) When two ideal polarizers are inserted between the bulb and the meter, with their axis of polarization making an angle of 90 degrees relative to each other, the transmitted intensity is given by Malus' Law. The initial intensity is 112.0 Cd, and the angle between the transmission axes of the polarizers is 90 degrees. Therefore:

Transmitted intensity = Initial intensity * (cos(90))^2
Transmitted intensity = 112.0 Cd * (0)^2
Transmitted intensity = 0 Cd

So, the intensity reading on the meter with two ideal polarizers at a 90-degree angle is 0 Cd.

e) When two ideal polarizers are inserted between the bulb and the meter, with their axis of polarization making an angle of θ = 4.0 degrees relative to each other, the transmitted intensity can be calculated using Malus' Law. The initial intensity is 112.0 Cd, and the angle between the transmission axes of the polarizers is 4.0 degrees. Therefore:

Transmitted intensity = Initial intensity * (cos(4))^2
Transmitted intensity = 112.0 Cd * (0.997564)^2
Transmitted intensity ≈ 111.74 Cd (rounded to two decimal places)

So, the intensity reading on the meter with two ideal polarizers at a 4-degree angle is approximately 111.74 Cd.

To answer these questions, we need to understand how a single ideal polarizer and multiple ideal polarizers affect the intensity of unpolarized light passing through them.

First, let's define the properties of an ideal polarizer:
- An ideal polarizer only allows light waves polarized in a specific direction to pass through.
- It absorbs or blocks light waves polarized in other directions.
- It does not affect the intensity of light waves polarized in the allowed direction.

Now let's go through each question one by one:

a) When a single ideal polarizer is inserted between the bulb and the meter, the intensity reading on the meter will be reduced. This is because the single polarizer will only allow light waves polarized in a specific direction to pass through, while absorbing or blocking light waves polarized in other directions.

The intensity of the light passing through the single polarizer can be calculated as follows:
Intensity after single polarizer = Initial intensity x (cosθ)^2
Here, θ represents the angle between the axis of polarization of the polarizer and the direction of the incident unpolarized light.

b) When two ideal polarizers are inserted between the bulb and the meter with their axis of polarization aligned (i.e., their polarization directions are parallel), the intensity reading on the meter will be further reduced compared to part (a). This is because with both polarizers aligned, only a fraction of the already polarized light passing through the first polarizer will be able to pass through the second polarizer.

The intensity of the light passing through the aligned polarizers can be calculated similarly:
Intensity after aligned polarizers = Initial intensity x (cosθ)^2 x (cosθ)^2

c) When two ideal polarizers are inserted between the bulb and the meter with their axis of polarization making an angle of 45° relative to each other, the intensity reading on the meter will be the same as in part (b). This is because the angle between the polarizers does not affect the intensity when their axis of polarization is aligned.

d) When two ideal polarizers are inserted between the bulb and the meter with their axis of polarization making an angle of 90° relative to each other (i.e., their polarization directions are perpendicular), no light will pass through the second polarizer. This is because the polarizers are oriented in such a way that light passing through the first polarizer is blocked entirely by the second polarizer. Therefore, the intensity reading on the meter will be zero.

e) When two ideal polarizers are inserted between the bulb and the meter with their axis of polarization making an angle of θ = 4.0° relative to each other, the intensity reading on the meter will be somewhere between the values obtained in part (b) and part (d). The exact calculation will depend on the specific angle and the initial intensity of the unpolarized light, which is not provided in the question.

To calculate the intensity in this case, you will use the formula:
Intensity after polarizers = Initial intensity x (cosθ)^2 x (cosθ)^2

Simply plug in the appropriate values into the formula to calculate the intensity reading on the meter.