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.