Question

Свет падает на дифракционную решетку. Определите расстояние между максимумом второго порядка и центральным максимумом, если длина волны падающего света равна 300нм. Расстояние от экрана до решетки 2 м. Решетка имеет 100штр/мм.

Answer 1

Для решетки
d*sina= л*k     k=2
при малых углах  sina=tga=h/L    L=2 м
d*h/L= л*2
h= 2*л*L/d=2*300*10^-9*2/10^-5=12*10^-2=12 см

Answer 2

Calculation of Distance between Second Order Maximum and Central Maximum

To calculate the distance between the second-order maximum and the central maximum when light falls on a diffraction grating, we can use the formula:

d * sin(θ) = m * λ

Where: - d is the spacing between the slits in the diffraction grating (in this case, given as 100 lines/mm, which is equivalent to 0.01 mm or 0.00001 m). - θ is the angle between the incident light and the normal to the grating. - m is the order of the maximum (in this case, the second order). - λ is the wavelength of the incident light (given as 300 nm, which is equivalent to 0.0003 mm or 0.0000003 m).

To find the distance between the second-order maximum and the central maximum, we need to find the angle θ. We can use the following formula to calculate the angle:

tan(θ) = y / L

Where: - y is the distance between the central maximum and the second-order maximum. - L is the distance between the diffraction grating and the screen (given as 2 m).

Let's calculate the distance between the second-order maximum and the central maximum step by step:

1. Convert the wavelength of the incident light to meters: 300 nm = 0.0000003 m. 2. Convert the spacing between the slits in the diffraction grating to meters: 100 lines/mm = 0.01 mm = 0.00001 m. 3. Calculate the angle θ using the formula: tan(θ) = y / L. 4. Rearrange the formula to solve for y: y = L * tan(θ). 5. Substitute the values of L (2 m) and θ into the equation to calculate y. 6. Calculate the distance between the second-order maximum and the central maximum by subtracting the value of y from the total distance between the diffraction grating and the screen (2 m).

Let's perform the calculations:

1. The wavelength of the incident light is 0.0000003 m. 2. The spacing between the slits in the diffraction grating is 0.00001 m. 3. Using the formula tan(θ) = y / L, we can rearrange it to θ = arctan(y / L). 4. Substituting the values of L (2 m) and θ into the equation, we can calculate y. 5. The distance between the second-order maximum and the central maximum is given by the equation: distance = L - y.

Let's calculate the values:

Using the given values: - λ = 0.0000003 m - d = 0.00001 m - L = 2 m

We can calculate θ using the formula tan(θ) = y / L:

θ = arctan(y / L)

Now, let's calculate y:

y = L * tan(θ)

Finally, we can calculate the distance between the second-order maximum and the central maximum:

distance = L - y

Please note that we need to calculate the value of θ first in order to proceed with the calculations.