Question

На дифракционную решетку, имеющую 600 штрихов на 1 мм, нормально падает свет от газоразрядной трубки. Дифракционный спектр рассматривается через зрительную трубку, установленную на лимбе. Красная линия в спектре первого порядка видна под углом 23 градусов, зеленая - под углом 20 градусов. Определить длины волн этих линий. Помогите пожалуйста!

Answer 1

Постоянная решетки d=1/600 мм = 10/6*10^-6 м 
максимум порядка n наблюдается когда оптическая разность d*sin(alpha) равна n длинам волн 
n*L=d*sin(alpha)
L=d*sin(alpha)/n
для красного цвета
L=10/6*10^-6*sin(23)/1 м = 6,51219E-07 м ~ 651 нм
для зеленого цвета
L=10/6*10^-6*sin(20)/1 м =  5,70034E-07 м ~ 570 нм

Answer 2

Determining the Wavelengths of the Red and Green Lines

To determine the wavelengths of the red and green lines in the diffraction spectrum, we need to use the information provided about the diffraction grating and the angles at which the lines are observed.

The diffraction grating has 600 lines per millimeter. This means that there are 600 equally spaced slits or grooves per millimeter on the grating.

The red line is observed at an angle of 23 degrees, and the green line is observed at an angle of 20 degrees. These angles are measured with respect to the normal (perpendicular) to the grating surface.

To find the wavelengths of the red and green lines, we can use the formula for the diffraction grating:

nλ = d * sin(θ)

Where: - n is the order of the diffraction (in this case, n = 1 for the first order) - λ is the wavelength of light - d is the spacing between the grating lines (in this case, d = 1/600 mm) - θ is the angle at which the line is observed (in this case, θ = 23 degrees for the red line and θ = 20 degrees for the green line)

Let's calculate the wavelengths of the red and green lines using this formula.

For the red line: n = 1, d = 1/600 mm, θ = 23 degrees

1 * λ_red = (1/600) * sin(23 degrees)

For the green line: n = 1, d = 1/600 mm, θ = 20 degrees

1 * λ_green = (1/600) * sin(20 degrees)

Now, let's calculate the values using the given angles and the formula:

λ_red = (1/600) * sin(23 degrees) λ_green = (1/600) * sin(20 degrees)

Using a calculator, we can find the values of the wavelengths:

λ_red ≈ 6.56 × 10^-7 meters λ_green ≈ 5.69 × 10^-7 meters

Therefore, the approximate wavelengths of the red and green lines in the diffraction spectrum are 6.56 × 10^-7 meters and 5.69 × 10^-7 meters, respectively.

Please note that these calculations are approximate and may vary slightly depending on the accuracy of the measurements and the assumptions made.