Question

ДАЮ 70 БАЛЛОВ!!!! расстояние между двумя когерентными источниками света, излучающими волны равной длины лямбда=440нм, l=1мм. определите расстояние от источников света до экрана, если расстояние между соседними интерференционными максимумами на экране дельта икс=2,2мм

Answer 1

d=1 мм =10^-3 м (расстояние между отверстиями) 

Δх=2,2*10^-3 м  λ=440*10^-9 м   L=?

Δx=L*λ/d      L=Δx*d/λ=2.2*10^-3*10^-3/440*10^-9=5 м

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Answer 2

Calculation of the Distance between Coherent Light Sources and the Screen

To determine the distance between the coherent light sources and the screen, we can use the formula for the interference pattern produced by two coherent sources:

d * sin(θ) = m * λ

Where: - d is the distance between the sources, - θ is the angle between the line connecting the sources and the line connecting a point on the screen to one of the sources, - m is the order of the interference maximum, - λ is the wavelength of the light.

In this case, we are given that the wavelength (λ) is 440 nm and the distance between neighboring interference maxima (Δx) is 2.2 mm.

To find the distance between the sources (d), we need to find the angle (θ) corresponding to the given Δx. We can use the small angle approximation, which states that for small angles, sin(θ) ≈ θ (in radians).

Let's calculate the angle (θ) first:

θ = Δx / L

Where: - Δx is the distance between neighboring interference maxima on the screen, - L is the distance from the sources to the screen.

Given that Δx = 2.2 mm and L = 1 mm, we can substitute these values into the equation:

θ = 2.2 mm / 1 mm = 2.2 radians

Now, we can rearrange the interference equation to solve for the distance between the sources (d):

d = (m * λ) / sin(θ)

Substituting the known values, we have:

d = (1 * 440 nm) / sin(2.2 radians)

Converting the wavelength to meters (1 nm = 10^-9 m) and performing the calculation:

d = (1 * 440 * 10^-9 m) / sin(2.2 radians) ≈ 2.0 * 10^-4 m

Therefore, the distance between the coherent light sources and the screen is approximately 2.0 * 10^-4 meters.

Please note that the calculation assumes ideal conditions and does not take into account any other factors that may affect the interference pattern.