Question

Дифракционная решетка с периодом 10–3 м расположена параллельно экрану на расстоянии 1м от него. Какого порядка максимум в спектре будет наблюдаться на экране на расстоянии 10 см от центра дифракционной картины при освещении решетки нормально падающим параллельным пучком света с длиной волны 550 нм? Считать sinα » tgα.

Answer 1

Считать sinα » tgα = 10см/1м = 10см/100см=0.1

d=10–3 м

λ=550 нм=550*10-9 м

 

d*sin α  = m*λ

m = d*sin α  / λ =10–3 *0.1 / 550*10-9 = 181. 8 округляем вниз  181

 

ответ 181

Answer 2

Calculation of the Diffraction Grating Order

To determine the order of the maximum observed in the diffraction pattern on the screen, we can use the formula:

mλ = d sin(θ)

where: - m is the order of the maximum - λ is the wavelength of light - d is the period of the diffraction grating - θ is the angle of diffraction

In this case, the diffraction grating has a period of 10^(-3) m and is located parallel to the screen at a distance of 1 m from it. The distance from the center of the diffraction pattern on the screen is 10 cm (0.1 m). The light incident on the grating is a parallel beam with a wavelength of 550 nm (550 x 10^(-9) m).

To find the angle of diffraction, we can use the small angle approximation sin(θ) ≈ tan(θ).

Let's calculate the order of the maximum:

mλ = d sin(θ)

mλ = d tan(θ)

mλ = d (h/L)

where: - h is the distance from the center of the diffraction pattern on the screen (0.1 m) - L is the distance between the grating and the screen (1 m)

Substituting the given values into the equation:

m * 550 x 10^(-9) m = 10^(-3) m * (0.1 m / 1 m)

Simplifying the equation:

m = (10^(-3) m * 0.1 m) / (550 x 10^(-9) m)

Calculating the value:

m ≈ 0.018

Therefore, the order of the maximum observed in the diffraction pattern on the screen, at a distance of 10 cm from the center, is approximately 0.018.

Please note that the small angle approximation sin(θ) ≈ tan(θ) was used in this calculation.