Given information:
- Distance between the coherent sources (d) = 0.18 mm
- Distance to the screen (L) = 80 cm = 800 mm
- Distance of the fourth bright fringe (x) = 10.8 mm

Calculating the wavelength of light:

We can use the formula for fringe separation in Young's double-slit experiment to find the wavelength of light.

Fringe separation formula:
The fringe separation (Δx) is given by the formula:
Δx = λL/d

where:
- Δx is the fringe separation
- λ is the wavelength of light
- L is the distance from the double-slit to the screen
- d is the distance between the slits

Substituting the given values:
We know that the fourth bright fringe is located at a distance of 10.8 mm from the central fringe. This means the fringe separation (Δx) is 10.8 mm.

Plugging in the values into the formula:
10.8 mm = λ * 800 mm / 0.18 mm

Solving for λ:
To find the value of λ, we rearrange the formula:
λ = Δx * d / L

Substituting the values:
λ = 10.8 mm * 0.18 mm / 800 mm

Calculating the value of λ:
λ = 0.00243 mm

Therefore, the wavelength of light is 0.00243 mm.

Coherent and Incoherent Addition of Waves:

Coherent Addition of Waves:
- In coherent addition of waves, the waves have a constant phase relationship with each other.
- This means that the crests and troughs of the waves align perfectly when they superpose.
- When two coherent waves interfere constructively, the amplitude of the resulting wave is the sum of the individual amplitudes.
- When two coherent waves interfere destructively, the amplitude of the resulting wave is the difference between the individual amplitudes.
- Examples of coherent sources of waves include laser light and waves produced by a single-frequency source.

Incoherent Addition of Waves:
- In incoherent addition of waves, the waves do not have a constant phase relationship with each other.
- The crests and troughs of the waves do not align perfectly when they superpose.
- When two incoherent waves interfere, the resulting wave may have a varying amplitude and phase.
- The amplitude of the resulting wave depends on the individual amplitudes and phases of the waves.
- Examples of incoherent sources of waves include light from a common light bulb and waves produced by multiple sources with different frequencies or phases.

Summary:
- We calculated the wavelength of light using the fringe separation formula in the Young's double-slit experiment.
- The wavelength was found to be 0.00243 mm.
- Coherent addition of waves refers to waves that have a constant phase relationship, while incoherent addition of waves refers to waves that do not have a constant phase relationship.