Question

Свет от газоразрядной трубы падает нормально на дифракционную решетку, имеющую 800 штрихов на мм. максимум первого порядкаа для красной линии виден под углом 30 градусов, а для зеленой под углом 24,8. чему равна разность длин волны для красной и зеленой линии

Answer 1

D*sina1=k*Lk
d*sina2=k*Lз
dD=d*(sina1-sina2)/k=125*10^-8*(0,5-0,419)/1=1,01*10^-7 м

Answer 2

Calculation of the Wavelength Difference for Red and Green Lines

To calculate the wavelength difference between the red and green lines, we need to use the information provided about the diffraction grating and the angles at which the maximum first-order diffraction is observed for each line.

Given: - The diffraction grating has 800 lines per millimeter. - The maximum first-order diffraction for the red line is observed at an angle of 30 degrees. - The maximum first-order diffraction for the green line is observed at an angle of 24.8 degrees.

To calculate the wavelength difference, we can use the formula:

Δλ = λ_red - λ_green = (sinθ_red - sinθ_green) / N

Where: - Δλ is the wavelength difference. - λ_red is the wavelength of the red line. - λ_green is the wavelength of the green line. - θ_red is the angle of diffraction for the red line. - θ_green is the angle of diffraction for the green line. - N is the number of lines per unit length of the diffraction grating.

Let's calculate the wavelength difference using the given values:

θ_red = 30 degrees θ_green = 24.8 degrees N = 800 lines per millimeter = 800,000 lines per meter

Using the formula, we have:

Δλ = (sinθ_red - sinθ_green) / N

Substituting the values:

Δλ = (sin(30) - sin(24.8)) / 800,000

Now, let's calculate the value of Δλ using the provided angles:

Δλ ≈ 1.2 x 10^-7 meters

Therefore, the wavelength difference between the red and green lines is approximately 1.2 x 10^-7 meters.

Please note that the calculation assumes the angles are measured in radians. If the angles are given in degrees, they need to be converted to radians before using them in the formula.