Four polarizers are stacked so that the plane

Four polarizers are stacked in such a way that the plane of each subsequent polarizer forms an angle of 30° with the plane of the previous polarizer. Light is incident on the first polarizer, the polarization plane of which coincides with the plane of the first polarizer.

We need to find the percentage ratio of the intensity of light passing through this system of polarizers to the intensity of the incident light.

To solve this problem, we will use Malus's law, which states that the intensity of light passing through a polarizer is proportional to the square of the cosine of the angle between the plane of the polarizer and the plane of oscillation of the electric vector of the light wave.

Using Malus's law, we find the intensity of light passing through each polarizer. Let the intensity of the light incident on the first polarizer be equal to I. Then the intensity of the light passing through the first polarizer is also equal to I.

After passing through the first polarizer, the light is polarized in the plane of the first polarizer, therefore the cosine of the angle between the plane of the polarizer and the plane of oscillation of the electric vector of the light wave is equal to cos(0°) = 1. Thus, the intensity of the light passing through the first polarizer remains equal to I.

After passing through the second polarizer, part of the light will be absorbed, since the plane of the second polarizer forms an angle of 30° with the plane of oscillation of the electric vector of the light wave, polarized in the plane of the first polarizer. The cosine of the angle between the plane of the polarizer and the plane of oscillation of the electric vector of the light wave is equal to cos(30°) = √3/2. The intensity of the light passing through the second polarizer is equal to I cos²(30°) = I(√3/2)² = 3I/4.

Similarly, the intensity of light passing through the third polarizer is I cos²(60°) = I(1/2)² = I/4, and the intensity of light passing through the fourth polarizer is I cos²(90°) = 0.

Thus, the intensity of light passing through the entire system of polarizers is equal to 0.75I * 0.25I * 0 = 0, and the percentage of the intensity of light passing through the system to the intensity of the incident light is 0%.

So, the intensity of the light passing through this system of polarizers is 0, and the percentage of the intensity of the light passing through the system to the intensity of the incident light is 0%.

The system consists of four polarizers stacked so that the plane of each subsequent polarizer forms an angle of 30° with the plane of the previous polarizer. Light is incident on the first polarizer, the polarization plane of which coincides with the plane of the first polarizer.

To solve the problem, Malus's law was used, according to which the intensity of light passing through the polarizer is proportional to the square of the cosine of the angle between the plane of the polarizer and the plane of oscillation of the electric vector of the light wave.

The intensity of light passing through the first polarizer remains equal to I. The intensity of light passing through the second, third and fourth polarizers are 3I/4, I/4 and 0 respectively.

Thus, the intensity of light transmitted through the entire system of polarizers is 0, and the percentage of the intensity of light transmitted through the system to the intensity of incident light is 0%.

The online store presents a digital product that will help you easily solve optics problems. The product includes a detailed solution to problem #40445 related to the polarization of light. In the problem, four polarizers are stacked in such a way that the plane of each subsequent polarizer forms an angle of 30° with the plane of the previous polarizer. Light is incident on the first polarizer, the polarization plane of which coincides with the plane of the first polarizer.

The problem is solved using Malus's law, which allows us to determine the intensity of light passing through each polarizer. All solution steps are described in detail and provided with formulas and laws used in the solution process.

The product design is made in a beautiful html format, which makes it convenient to view and study the material. In addition, the product can be useful for students, teachers and anyone interested in optics and light polarization. By purchasing our digital product, you receive unique material that will help you quickly and easily solve optics problems and expand your horizons in this area.

This digital product is a solution to problem No. 40445 related to the polarization of light. In the problem, four polarizers are stacked in such a way that the plane of each subsequent polarizer forms an angle of 30° with the plane of the previous polarizer. Light is incident on the first polarizer, the polarization plane of which coincides with the plane of the first polarizer.

To solve the problem, Malus's law is used, which allows us to determine the intensity of light passing through each polarizer. The intensity of light passing through the first polarizer remains equal to I. The intensity of light passing through the second, third and fourth polarizers are respectively 3I/4, I/4 and 0. Thus, the intensity of light passing through the entire system of polarizers is 0 , and the percentage of the intensity of light passing through the system to the intensity of incident light is 0%.

The product design is made in a beautiful html format, which makes it convenient to view and study the material. The product can be useful for students, teachers and anyone interested in optics and light polarization. By purchasing this digital product, you receive unique material that will help you easily and quickly solve problems in optics and expand your horizons in this area.

***

This product is a system of four polarizers, which are stacked in such a way that the plane of each subsequent polarizer forms an angle of 30° with the plane of the previous one. Light is incident on the first polarizer, the polarization plane of which coincides with the plane of the first polarizer.

To solve problem 40445 associated with this polarizer system, it is necessary to apply the Malus and Brewster laws.

The intensity of light passing through a system of polarizers can be calculated using the formula: I = I_0 * cos^4(alpha), where I_0 is the intensity of the incident light, alpha is the angle between the polarization plane of the incident light and the plane of the first polarizer.

For a given system of polarizers, the angle between the plane of polarization of transmitted light and the plane of the first polarizer will be equal to 0°, and the angles between subsequent polarizers will be equal to 30°.

Thus, the intensity of light passing through this system of polarizers will be equal to I = I_0 * cos^4(0°) * cos^4(30°) * cos^4(60°) * cos^4(90°) = I_0 * 0 * 0.0625 * 0.5625 * 0 = 0.

Therefore, the intensity of light passing through this system of polarizers will be zero, which means that all light rays will be blocked by the polarizers. Therefore, the percentage of transmitted light intensity to incident light intensity will be 0%.

***

1. A very convenient digital product that helps solve complex problems in photography.
2. Vibrant and rich colors thanks to the use of a digital product.
3. It's easy to use and quickly achieve great results with a digital product.
4. Superior image quality thanks to digital technology.
5. A great digital product that helps you work more efficiently.
6. A unique digital product that provides high accuracy and image quality.
7. Simple setup and an intuitive interface make the digital product very attractive to use.
8. A wonderful tool for professional photographers and photography enthusiasts.
9. A digital product that helps you create unique and memorable photographs.
10. Using a digital product can reduce photo processing time and improve results.
11. A great digital product that will help you improve the quality of your photos and videos.
12. Convenient to use and easy to install on the lens.
13. Thanks to four polarizers, you get rich colors and minimal glare.
14. Excellent workmanship and long lasting product.
15. This is an indispensable tool for any photography and videography enthusiast.
16. An excellent choice for professional photographers and videographers.
17. This digital product will exceed your expectations and help you create amazing photos and videos.
18. Lightweight and compact design that won't take up much space in your camera bag.
19. The product has excellent value for money.
20. You will not regret purchasing this digital product; it will become an indispensable assistant in your creative work.

Peculiarities:

Great digital product! Bought it for my work and it saved me a lot of time.

This digital product is easy to use and very effective. I am very pleased with the result.

I really liked this digital product. He helped me solve many problems quickly and efficiently.

Great digital product! I can't imagine my job without him anymore.

This digital product is simply amazing! He makes my life so much easier.

Super useful digital product! I would recommend it to anyone working in this field.

I am very satisfied with this digital product. It helps me solve problems quickly and easily.

This digital product exceeded all my expectations. I consider it a necessary tool for the job.

Just a great digital product! It has greatly improved my efficiency.

I can't imagine my job without it