A quartz glass is placed between two parallel nicols.

Between two parallel polarizers there is a quartz plate 1 mm thick, which is cut parallel to the optical axis. In this case, the plane of polarization of monochromatic light incident on the first polarizer rotated by an angle of 20°. It is necessary to determine the minimum thickness of the plate at which light does not pass through the analyzer.

The problem is solved using Malus's law, which states that the intensity of light transmitted through the analyzer is proportional to the cosine of the square of the angle between the polarization planes of the analyzer and the polarizer.

Let I_0 be the initial intensity of light passing through the first polarizer. Then, after passing through the quartz plate, the light intensity will be equal to I = I_0 * cos^2(α), where α is the rotation angle of the light polarization plane.

Thus, in order for light not to pass through the analyzer, it is necessary that the angle between the polarization planes of the analyzer and the polarizer be 90 degrees, that is, cos^2(α) = 0. This means α = 45 degrees.

The thickness of the quartz plate is determined by the formula: d = λ/(2ncos(α)), where λ is the wavelength of light, n is the refractive index of quartz.

Substituting the values ​​into the formula, we get: d = λ/(2ncos(α)) = λ/(2ncos(45°)) = λ/(2nsqrt(2)/2) = λ/(n*sqrt(2))

Thus, the minimum thickness of the plate at which light does not pass through the analyzer is equal to λ/(n*sqrt(2)).

Quartz Light Polarization Plate is a digital product available in our digital product store. This plate is intended for use in optical experiments and research.

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Quartz plate for polarizing light

This digital item is intended for use in optical experiments and research. It is a thin quartz plate that is placed between two parallel polarizers.

The quartz plate has unique properties that allow it to polarize light. Using this product, you can conduct many interesting experiments and studies related to the polarization of light.

In addition, this plate has a minimum thickness at which light does not pass through the analyzer, which makes it an indispensable tool in optical experiments.

Buy Quartz Light Polarization Plate from our digital store and discover the world of optical research!

Quartz light polarization plate is a product designed for use in optical experiments and research. It is a thin quartz plate of thickness d, which is placed between two parallel polarizers. In this case, the plane of polarization of monochromatic light incident on the first polarizer is rotated by an angle of 20°.

In order for light not to pass through the analyzer, it is necessary that the angle between the polarization planes of the analyzer and the polarizer be 90 degrees, that is, cos^2(α) = 0. This means α = 45 degrees.

The minimum plate thickness at which light does not pass through the analyzer is determined by the formula: d = λ/(2n*cos(α)), where λ is the wavelength of light, n is the refractive index of quartz.

Substituting the values, we get: d = λ/(2ncos(45°)) = λ/(2nsqrt(2)/2) = λ/(n*sqrt(2)).

Thus, the minimum thickness of the plate at which light does not pass through the analyzer is equal to λ/(n*sqrt(2)).

Answer: the minimum plate thickness is λ/(n*sqrt(2)).

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This product is a quartz plate, which is used in optics as a polarizer. The plate has a thickness that can vary depending on the required parameters. In this case, to solve problem 40184, you need to find the minimum thickness of the plate at which light will not pass through the analyzer.

To do this, it is necessary to place a quartz plate between two parallel nicols and rotate the plane of polarization of monochromatic light at an angle of 20°. Then you need to find the thickness of the plate at which light will not pass through the analyzer.

To solve this problem, the laws of optics and Fresnel's formulas are used. In particular, the Malus law is used to calculate the angle of rotation of the plane of polarization, and the Fresnel formula is used to determine the thickness of the plate at which light will not pass through the analyzer.

So, the Fresnel formula for determining the thickness of the plate is as follows:

t = λ/4n,

where t is the thickness of the plate, λ is the wavelength of light, n is the refractive index of the plate material.

To solve the problem, it is necessary to find the minimum plate thickness at which light will not pass through the analyzer. This means that the plane of polarization of light passing through the plate must be perpendicular to the plane of polarization of the analyzer.

Thus, to find the minimum thickness of the plate, you need to find the value at which the angle of rotation of the plane of polarization becomes equal to 90°. Substituting this value into the Fresnel formula, we get:

t = λ/2n.

Answer: The minimum thickness of a quartz plate at which light will not pass through the analyzer is equal to half the wavelength of the light divided by the refractive index of the plate material: t = λ/2n.

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