Calculation of the Wavelength of the Incoming Light

The behavior of light can be studied through the phenomenon of interference. When a monochromatic light is directed at a surface, the resulting interference patterns can reveal the properties of the light as well as the medium it travels through.

In your case, the experiment involves a light source directed normally at the surface of a plate. The light interacts with the plate and forms a series of concentric rings, with the center being a dark spot. The fourth dark ring, with a radius of 4.5 mm, is the last ring before the central spot.

Deriving the Formula for the Radius of the Dark Rings

Once the radius of the fourth ring is known, it can be used to determine the wavelength of the light. The radius of the nth dark ring can be mathematically expressed as follows:

R_n = √nλR

where R_n is the radius of the nth dark ring, λ is the wavelength of light, and R is the radius of curvature of the lens.

In our case, the equation can be rewritten as:

R₄ = √4λ(8,6)

Simplifying the equation, we get:

4,5 mm = 2√λ(8,6)

Now, by solving for λ, we obtain the wavelength of the incoming light:

λ = (4,5 mm)²/34,96 mm

This gives us a value of 0.625 mm, which is the wavelength of the monochromatic light source used in the experiment.

The energy, or энергия фотонов, of photons is given by the formula E = hc/λ, where h is Planck's constant and λ is the wavelength of light. Assuming a monochromatic light with a wavelength of 0.165 microns, we can calculate the energy to be approximately 7.56 × 10^-19 Joules.

Now, let's look at the potential of the charged copper ball, or потенциал зарядения шарика. When light shines on a metal surface, it can cause electrons to be emitted, a phenomenon known as the photoelectric effect. The work function, or работа выхода электрона, for copper is given as 7.2 × 10^-19 Joules. This means that each photon must have at least this energy in order to be able to knock an electron out of the metal surface. Any excess energy will be converted into kinetic energy of the electron.

As for the charging of the ball, it will depend on the number and energy of the photons hitting the surface. If we assume that the copper ball is initially neutral, each photon with enough energy can knock out an electron and leave a positive charge behind. This will continue until the electrons on the surface have accumulated enough energy to repel any more incoming photons. At this point, the ball will reach a steady state with a certain amount of charge.

So, to summarize:

• The energy of the photons is approximately 7.56 × 10^-19 Joules.
• The potential of the charged copper ball will depend on the number and energy of incoming photons, but it will reach a steady state eventually.

Answer: The wavelength of the incident light can be calculated using the formula λ = d * sin(θ), where d is the distance between the lines on the diffraction grating and θ is the angle between the diffracted beams. In this case, d = 1 mm and θ = 8° for the first order spectra.

Substituting the values in the formula, we get:

λ = (1 mm) * sin(8°) = 0.139 mm or 139 nm

Therefore, the wavelength of the monochromatic light incident on the diffraction grating is approximately 139 nm.