Question

Для определения длины световой волны применена дифракционная решетка с периодом 0, 01 мм. Первое дифракционное изображение на экране получено на расстоянии 11,8 см от центрального и на расстояних 2 м от решетки. Найдите длину световой волны.

Answer 1

Дано:
d=0,01мм=10⁻⁵м  (период решетки)
k=1   9порядок спектра0
b=11,8см = 0,118м
a=2м
λ=db/ka
λ=(10⁻⁵м·0,118м)/(1·2м)=0,059·10⁻⁵м=5,9·⁻⁷м
Ответ: 5,9·10⁻⁷м

Answer 2

Determining the Wavelength of Light using a Diffraction Grating

To determine the wavelength of light, a diffraction grating with a period of 0.01 mm was used. The first diffraction image on the screen was obtained at a distance of 11.8 cm from the central point, and at distances of 2 m from the grating. We need to find the wavelength of the light.

To solve this problem, we can use the formula for the diffraction pattern produced by a diffraction grating:

d * sin(θ) = m * λ

Where: - d is the period of the diffraction grating (0.01 mm or 0.01 * 10^-3 m), - θ is the angle of diffraction, - m is the order of the diffraction maximum (in this case, m = 1), - λ is the wavelength of light.

We can rearrange the formula to solve for the wavelength:

λ = d * sin(θ) / m

Now, let's calculate the wavelength of the light.

Given: - Period of the diffraction grating (d) = 0.01 mm = 0.01 * 10^-3 m - Distance from the central point to the first diffraction image (L) = 11.8 cm = 11.8 * 10^-2 m - Distance from the grating to the screen (x) = 2 m

To find the angle of diffraction (θ), we can use the small angle approximation:

θ = tan(θ) = L / x

Substituting the given values, we have:

θ = 11.8 * 10^-2 m / 2 m

Calculating the value of θ, we get:

θ ≈ 0.059

Now, we can substitute the values of d, θ, and m into the formula to find the wavelength (λ):

λ = (0.01 * 10^-3 m) * sin(0.059) / 1

Calculating the value of λ, we get:

λ ≈ 5.9 * 10^-7 m

Therefore, the wavelength of the light is approximately 5.9 * 10^-7 m.