Final answer:
The phase difference between waves from the top and one third from the bottom of a single slit can be found using the path difference and the relationship between phase difference and path difference, using the wavelength of the light.
Step-by-step explanation:
To find the phase difference between waves from the top and one third from the bottom of the slit to a point on the screen, we need to use the path difference between these two points of the wave originating from the single slit.
The path difference (ΔL) can be calculated using the formula ΔL = d sin θ, where d is the distance between the two points on the slit and θ is the angle of diffraction.
The slit width is 2100 nm, and we are interested in the path difference between the top and the point one third from the bottom, which is ⅓ of the slit width, or 700 nm.
Using the small angle approximation (since the screen is much further away than the width of the slit), θ can be approximated by tan θ, which is the vertical distance (10.0 cm) over the horizontal distance (2.0 m) from the center of the pattern.
Once θ is found, ΔL = (700 nm) sin(θ) can be calculated.
The phase difference (φ) is related to the path difference by the equation φ = (2π/λ)(ΔL), where λ is the wavelength of the light (632.8 nm).
This will give the phase difference in terms of π.