The Polarizer | Physics with Professor Matt Anderson | M28-17

Physics with Professor Matt Anderson
14 Mar 202206:26
EducationalLearning
32 Likes 10 Comments

TLDRThe video script discusses the concept of polarizers and Malus's Law in the context of unpolarized light passing through a polarizer. The scenario involves sunlight, which is unpolarized, being filtered through an ideal polarizer with its transmission axis at a 30-degree angle to the vertical. The script explains that only half of the initial light intensity passes through the first polarizer due to the vertical polarization, and then applies Malus's Law to calculate the final intensity after passing through the polarizer, resulting in 5 watts per square meter from the initial 10 watts per square meter.

Takeaways
  • 🔆 The problem involves an ideal polarizer with its transmission axis at a 30-degree angle to the vertical, placed in a beam of unpolarized light with an intensity of 10 watts per square meter.
  • 📚 Malus's Law is introduced as the key principle to solve the problem, stating that the intensity of light after passing through a polarizer is proportional to the cosine squared of the angle (theta) between the light's polarization and the polarizer's transmission axis.
  • 🤔 The discussion clarifies that Malus's Law was initially taught with two polarizers, but here it's applied to a single polarizer scenario, which initially seems different but is fundamentally the same.
  • 🌞 Unpolarized light, like sunlight, has equal intensities in all directions and does not have a specific polarization direction, making it different from polarized light.
  • 📉 The first polarizer only allows vertical polarization to pass through, effectively reducing the intensity of the light by half, from the original intensity (I_sun) to I_not.
  • 📐 The angle of the polarizer's transmission axis relative to the vertical does not affect the intensity of the unpolarized light passing through it, as the light is not polarized in any particular direction.
  • ⚖️ The intensity of light after passing through the polarizer is calculated by taking half of the original intensity (I_sun) due to the first polarizer's effect, which eliminates the horizontal component of the light.
  • 🧭 The final intensity (I) of the light after passing through the polarizer is calculated as I_sun divided by 2, which in this case is 5 watts per square meter, given I_sun is 10 watts per square meter.
  • 📝 The problem-solving approach involves understanding the effect of a polarizer on unpolarized light and applying Malus's Law correctly, considering the initial intensity and the angle of the polarizer.
  • 👓 A practical example of using polarized sunglasses to look at the sun is given to illustrate that the angle of the polarizer does not make the sun appear dimmer, emphasizing the concept of unpolarized light.
  • 🔍 The script emphasizes the importance of understanding the difference between polarized and unpolarized light and how this affects the calculation of light intensity after passing through a polarizer.
Q & A

  • What is the purpose of a polarizer in optics?

    -A polarizer is used to filter light waves so that only waves vibrating in a specific direction pass through. It can convert unpolarized light into polarized light.

  • What is meant by the term 'unpolarized light'?

    -Unpolarized light refers to light waves that vibrate in multiple directions or orientations, such as sunlight.

  • What is Malus's law and how is it applied in this context?

    -Malus's law states that the intensity of light passing through a polarizer is given by \( I = I_0 \cdot \cos^2(\theta) \), where \( I_0 \) is the initial intensity, and \( \theta \) is the angle between the light's polarization direction and the polarizer's transmission axis.

  • Why is the first polarizer in the script described as having the purpose of only letting through vertical polarization?

    -The first polarizer is described this way to illustrate that it filters out all but the vertically polarized light, which is essential for understanding how the second polarizer affects the light intensity.

  • What is the significance of the polarizer being rotated 30 degrees relative to the vertical in the problem?

    -The rotation of the polarizer affects the angle \( \theta \) in Malus's law. However, since the light is unpolarized, the initial polarization direction does not matter, and the problem remains the same as if the polarizer was vertical.

  • How does the orientation of the polarizer's transmission axis affect the intensity of the light that passes through it?

    -The orientation of the polarizer's transmission axis determines the angle \( \theta \) in Malus's law, which directly affects the intensity of the light that passes through. The intensity is maximized when the axis is aligned with the light's polarization direction and minimized when they are perpendicular.

  • What is the initial intensity of the unpolarized light in the script?

    -The initial intensity of the unpolarized light, denoted as \( I_{sun} \), is given as 10 watts per square meter.

  • How much of the unpolarized light's intensity gets through the first polarizer?

    -Since the first polarizer filters out the horizontal polarization, only half of the unpolarized light's intensity, which is 5 watts per square meter, gets through.

  • What is the final intensity of the light after passing through the polarizer with its transmission axis rotated 30 degrees?

    -The final intensity is the same as if the polarizer were vertical because the light is unpolarized. It is half of the initial intensity, which is 5 watts per square meter.

  • Why does the rotation of the polarizer not affect the intensity of the light from an unpolarized source?

    -The rotation of the polarizer does not affect the intensity of light from an unpolarized source because unpolarized light contains an equal mix of all polarization directions, so any rotation of the polarizer will still allow the same amount of light to pass through on average.

  • What would happen if the light were polarized instead of unpolarized in this scenario?

    -If the light were polarized, the orientation of the polarizer's transmission axis relative to the light's polarization direction would significantly affect the intensity of the light that passes through, following Malus's law.

Outlines
00:00
🔆 Understanding Polarization and Malus' Law

This paragraph introduces the concept of a polarizer and its effect on unpolarized light. It discusses Malus' Law, which describes the intensity of light after passing through a polarizer. The scenario involves sunlight, which is unpolarized, passing through a polarizer with its transmission axis at a 30-degree angle to the vertical. The teacher seeks to understand the intensity of light after passing through the polarizer by considering the initial polarization state of the light and the orientation of the polarizer. The importance of Malus' Law in calculating the transmitted intensity is highlighted, and the teacher engages a student named Eudoria to discuss the application of the law in this context.

05:01
🌟 Calculating Light Intensity After Polarization

The second paragraph delves into the practical application of the concepts introduced in the first. It addresses the question of whether the orientation of the polarizer affects the intensity of unpolarized light, such as sunlight. The teacher clarifies that since sunlight is unpolarized, rotating the polarizer does not change the perceived brightness. The focus then shifts to calculating the intensity of light after passing through the polarizer, given that the initial intensity is 10 watts per square meter. The teacher explains that since the polarizer only allows vertical polarization to pass through, and unpolarized light has equal amounts of vertical and horizontal polarization, half of the light's intensity is transmitted through the first polarizer. The final step is to apply Malus' Law to find the intensity after the light has passed through the polarizer at a 30-degree angle, which is not directly calculated in the paragraph but set up for the next step in the explanation.

Mindmap
Keywords
💡Polarizer
A polarizer is an optical filter that allows light waves of a specific orientation to pass through while blocking others. In the context of the video, the polarizer is used to demonstrate how light intensity changes when unpolarized light passes through it. The script discusses an ideal polarizer with its transmission axis rotated to 30 degrees relative to the vertical, which is central to understanding the light's behavior after passing through the polarizer.
💡Transmission Axis
The transmission axis of a polarizer is the direction along which the polarizer allows light waves to pass. It is depicted in the script with an arrow on a circle, indicating the orientation of the filter. The angle of the transmission axis relative to the vertical is crucial in determining the intensity of light that gets through the polarizer, as seen with the 30-degree rotation in the example.
💡Unpolarized Light
Unpolarized light is light that consists of waves vibrating in all possible perpendicular directions to the direction of propagation. The script mentions sunlight as an example of unpolarized light, which has no specific polarization orientation and is the starting point for the demonstration of how a polarizer affects light intensity.
💡Intensity
In the context of optics, intensity refers to the amount of light energy passing through a unit area, measured in watts per square meter. The script discusses the initial intensity of the unpolarized light beam as 10 watts per square meter and how this value changes after passing through the polarizer.
💡Malus's Law
Malus's Law is a principle in optics that describes the intensity of light after passing through a polarizer. It states that the transmitted light intensity is proportional to the square of the cosine of the angle between the light's polarization and the polarizer's transmission axis. In the script, Malus's Law is used to calculate the intensity of light after it has passed through the polarizer at a 30-degree angle.
💡Cosine Squared
The term 'cosine squared' in the script refers to the mathematical operation of squaring the cosine of an angle, which is used in Malus's Law to determine the intensity of light transmitted through a polarizer. It is a key component in the formula for calculating the intensity of polarized light.
💡Vertical Polarization
Vertical polarization refers to light waves that vibrate in a vertical plane. In the script, the first polarizer is described as allowing only vertically polarized light to pass through, which sets the stage for the demonstration of Malus's Law with a second polarizer at an angle.
💡Horizontal Polarization
Horizontal polarization is the orientation of light waves vibrating in a horizontal plane. The script explains that a polarizer can eliminate horizontal polarization, which is important for understanding how unpolarized light is reduced to a single polarization direction by a polarizer.
💡Sunlight
Sunlight is used in the script as an example of unpolarized light. It serves as a practical and familiar reference for the viewer to understand the concept of polarization and how a polarizer affects the intensity of light. The script uses sunlight to illustrate the initial state of the light before it passes through the polarizer.
💡Polarized Sunglasses
Polarized sunglasses are a type of eyewear that uses polarizers to reduce glare and enhance visual clarity. In the script, they are mentioned as an example of a polarizer in everyday use, helping to explain the concept of polarization in a relatable context.
Highlights

Introduction of a polarizer question involving the transmission of unpolarized light.

Explanation of an ideal polarizer and its orientation at 30 degrees relative to the vertical.

Description of the unpolarized light source, such as sunlight, and its intensity.

Introduction of Malus's law for calculating the intensity of light after passing through a polarizer.

Malus's law formula presented as I = I₀ * cos²(θ).

Clarification on the purpose of the first polarizer in the context of Malus's law.

Discussion on the effect of the first polarizer allowing only vertical polarization.

Explanation of the relationship between the intensity of sunlight and the transmitted intensity after the first polarizer.

Mention of the factor of 1/2 for the intensity of unpolarized light passing through the first polarizer.

Analysis of the impact of the polarizer's orientation on the transmitted light intensity.

Illustration of the concept that the unpolarized nature of sunlight makes its intensity unaffected by the polarizer's angle.

Calculation of the transmitted intensity as half of the initial intensity of the unpolarized light.

Final answer provided: the transmitted intensity is 5 watts per square meter after passing through the polarizer.

Emphasis on the importance of understanding the polarization state of light in relation to polarizers.

Highlighting the practical application of polarizers in everyday scenarios, such as sunglasses.

Transcripts

Browse More Related Video

Physics 53 Polarization (4 of 5) Ninety Polarizers

Physics 53 Polarization (2 of 5) Two Polarizers

Physics 53 Polarization (3 of 5) Three Polarizers

Time of Flight in Projectile Motion | Physics

Where Does The Range Equation Come From?

Area of an Oblique Triangle - SAS & SSS - Heron's Formula, Trigonometry

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
PolarizationMalus's LawUnpolarized LightLight IntensityOpticsPhysicsEducationalSunlightPolarizerCosine Squared