Final answer:
The distance between the bright fringes can be calculated using the formula x = (m * λ * D) / d. The phase difference between the last two points of the waves can be calculated using the formula Δφ = 2π * Δx / λ'. Destructive interference occurs when the phase difference is an odd multiple of π (pi), and constructive interference occurs when the phase difference is an even multiple of π (pi).
Step-by-step explanation:
The distance between the central bright fringe on the screen and the point where a bright fringe from one interference pattern coincides with a bright fringe from the other can be calculated using the formula: x = (m * λ * D) / d, where x is the distance, m is the order of the fringe, λ is the wavelength, D is the distance between the screen and the slits, and d is the distance between the slits. Plugging in the values, we have: x = (1 * 820 nm * 2 m) / 3 mm = 1.093 m. Therefore, the bright fringes will coincide at a distance of 1.093 m from the central bright fringe on the screen.
The phase difference between the last two points of the two waves can be calculated using the formula: Δφ = 2π * Δx / λ', where Δφ is the phase difference, Δx is the distance between the last two points, and λ' is the wavelength of the second mixture of wavelengths. Plugging in the values, we have: Δφ = 2π * (1.093 m) / 900 nm = 7.278 radians. Therefore, the phase difference between the last two points is 7.278 radians.
If the phase difference is an odd multiple of π (pi), destructive interference will occur. If the phase difference is an even multiple of π (pi), constructive interference will occur.