Question

На дифракционную решетку с периодом 0,001 мм падает белый свет. На экране, находящимся на расстоянии 1м от решетки образуются картина дифракции света. Определите расстояние на экране между первым и вторым максимумом красного света лямда = 750нм

Answer 1

Условие максимума для дифракционной решетки:

Δk λ = d sin(Δα)

будем считать, что значение sin(Δα) мало. тогда sin(Δα) ≈ tg(Δα) = Δb/L. тогда

λ = (d Δb)/L

Δb = (λ L)/d

Answer 2

Calculation of the Distance between the First and Second Maximum of Red Light on the Screen

To calculate the distance between the first and second maximum of red light on the screen, we need to consider the properties of diffraction grating and the wavelength of the red light.

Given: - Period of the diffraction grating (d) = 0.001 mm = 0.000001 m - Distance between the diffraction grating and the screen (L) = 1 m - Wavelength of red light (λ) = 750 nm = 0.00000075 m

The formula to calculate the angular position of the maximum for a diffraction grating is:

sin(θ) = mλ / d,

where: - θ is the angular position of the maximum, - m is the order of the maximum, - λ is the wavelength of light, and - d is the period of the diffraction grating.

To find the distance between the first and second maximum on the screen, we need to calculate the angular positions of the first and second maximum for red light using the given values.

Let's calculate the angular position of the first maximum (m = 1):

sin(θ₁) = (1 * 0.00000075) / 0.000001.

Using a scientific calculator, we can find that θ₁ ≈ 0.75 radians.

Similarly, let's calculate the angular position of the second maximum (m = 2):

sin(θ₂) = (2 * 0.00000075) / 0.000001.

Again, using a scientific calculator, we can find that θ₂ ≈ 1.5 radians.

Now, to find the distance between the first and second maximum on the screen, we can use the formula:

Distance = L * (θ₂ - θ₁).

Substituting the values, we get:

Distance = 1 * (1.5 - 0.75) ≈ 0.75 meters.

Therefore, the distance between the first and second maximum of red light on the screen is approximately 0.75 meters.

Please note that the calculations provided are based on the given values and assumptions.