Question

Дифракционная решетка имеющая 200 штрихов на 1 мм, освещается синим светом.Определите длину световой волны и ее частоту, если первый максимум виден под углом 5*30'?

Answer 1

Найдем период дифракционной решетки:
a = 1/200 = 0,005 мм  или
a = 5*10⁻⁶ м

Формула дифракционной решетки:
a*sinφ = m*λ

Длина волны:
λ =a*sinφ/m = 5*10⁻⁶*sin 5°30' / 1 ≈ 5*10⁻⁶*0,0958 ≈ 480 нм

Частота:
υ = с/λ = 3*10⁸/480*10⁻⁹ ≈ 6,3*10¹⁴ Гц

Answer 2

Calculating Wavelength and Frequency of Light Using Diffraction Grating

To calculate the wavelength and frequency of light using a diffraction grating, we can use the formula:

d*sin(θ) = m*λ

Where: - d is the distance between slits on the diffraction grating - θ is the angle of diffraction - m is the order of the maximum - λ is the wavelength of light

Given: - Number of slits on the diffraction grating, N = 200 per millimeter - Angle of the first maximum, θ = 5°30'

First, we need to convert the angle to decimal degrees: 5°30' = 5 + 30/60 = 5.5°

Now, we can calculate the wavelength of the light using the given information.

Using the formula d*sin(θ) = m*λ, we can solve for the wavelength λ.

Given that d = 1/N = 1/200 mm = 0.005 mm (or 0.000005 m), and θ = 5.5°:

0.000005 * sin(5.5°) = 1 * λ

Let's calculate the value of λ using the given information.

0.000005 * sin(5.5°) = 1 * λ λ = 0.000000478 m

So, the calculated wavelength of the light is 0.000000478 meters.

Now, to find the frequency of the light, we can use the formula:

c = λ*f

Where: - c is the speed of light in a vacuum (c = 3.00 x 10^8 m/s) - λ is the wavelength of light - f is the frequency of light

Let's calculate the frequency of the light using the calculated wavelength.

3.00 x 10^8 = 0.000000478 * f

f = (3.00 x 10^8) / 0.000000478

f ≈ 6.28 x 10^14 Hz

So, the calculated frequency of the light is approximately 6.28 x 10^14 Hz.