A thin transparent plate is illuminated by normal incidence

It is necessary to find the minimum difference in the path of rays reflected from the surface of a thin transparent plate, at which it will look orange in reflected light, provided that the plate is illuminated with normally incident white light. The wavelength of orange light is 600 nm. The answer must be given in nanometers.

Solution tasks:

First you need to determine the thickness of the plate. When reflected from the surface of a thin plate, the rays interfere, which leads to the appearance of a color pattern. The color we observe depends on the path difference between the reflected rays.

The path difference between the reflected rays can be expressed by the following formula:

Δ = 2 * d * cos(θ)

where Δ is the path difference, d is the thickness of the plate, θ is the angle of incidence of light on the surface of the plate.

To find the minimum path difference, it is necessary that the path difference between the beams be equal to the wavelength of the orange light. Thus we get the equation:

2 * d * cos(θ) = λ,

where λ = 600 nm is the wavelength of orange light.

The minimum thickness of the plate can be found by setting cos(θ) = 1, since this will give the smallest value of the path difference. Thus we get:

2 * d = λ,

d = λ/2 = 300 nm.

Answer: 300 nm.

Product Description: Thin transparent plate

We present to your attention a digital product - a thin transparent plate, which is illuminated by normally incident white light.

This plate is an ideal choice for those interested in optics and physics. When light is reflected from its surface, rays interfere, which leads to the appearance of a beautiful color pattern.

The thickness of the plate is 300 nm, which makes it possible to observe the minimum difference in the path of the rays, at which the plate appears orange in reflected light. The wavelength of orange light is 600 nm.

This digital product is ideal for teaching and experimenting in optics and physics.

We present to you a digital product - a thin transparent plate, ideal for experiments in the field of optics and physics. The plate is illuminated by normally incident white light, and when the light is reflected from its surface, the rays interfere, which leads to the appearance of a beautiful color picture.

To find the smallest difference in the path of rays reflected from the surface of the plate, at which it will look orange in reflected light, it is necessary to determine the thickness of the plate. The path difference between the reflected rays can be expressed by the formula: Δ = 2 * d * cos(θ), where Δ is the path difference, d is the thickness of the plate, θ is the angle of incidence of light on the surface of the plate.

To find the minimum path difference, it is necessary that the path difference between the beams be equal to the wavelength of orange light, that is, Δ = λ, where λ = 600 nm is the wavelength of orange light.

Assuming cos(θ) = 1, we obtain the minimum plate thickness: 2 * d = λ, d = λ/2 = 300 nm.

Thus, the answer to the problem: the smallest ray path difference at which the plate will look orange in reflected light is 600 - 300 = 300 nm.

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This product describes a physical problem involving a thin transparent plate that is illuminated by normally incident white light. The task is to find the smallest difference in the path of the rays reflected from the surface of the plate, at which the plate in the reflected light appears orange at a wavelength of orange light of 600 nm. The answer must be given in nanometers.

To solve this problem, we can use the formula to find the path difference between rays passing through a thin transparent plate that has a thickness d:

Δ = 2d(cosθ - cosφ),

where θ is the angle of incidence of the beam, φ is the angle of refraction of the beam.

Under certain conditions, the path difference can cause the beams to interfere, which can cause the color of the light to change. In this problem, you need to find the smallest path difference at which the plate appears orange in reflected light at a wavelength of orange light of 600 nm.

To find the smallest path difference at which the color of the reflected light turns orange, you can use the following formula:

Δ = ml/2,

where m is an integer (called the order of interference), λ is the wavelength of light.

Thus, to find the smallest path difference, you need to solve the equation:

2d(cosθ - cosφ) = mλ,

where m = 1, since the smallest path difference is required for the orange light.

By solving this equation for the thickness of the plate d, we will find the answer to the problem.

I hope this description will help you solve this problem. If you have any questions about the solution, please feel free to ask.

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