Final answer:
To determine the number of bright fringes in the central diffraction maximum for a double-slit setup, calculate the angle of the first diffraction minimum, find the total angular width of the central maximum, and count the number of m integer values that fit within this angular range, representing the interference fringes. The exact number for the given parameters cannot be given without performing the actual calculations.
Step-by-step explanation:
Double-Slit Diffraction Calculation
To determine the number of bright interference fringes within the central diffraction maximum for light passing through a double-slit, we can make use of the double-slit interference formula:
Calculate the angle θ corresponding to the first minimum of the single-slit diffraction pattern using the formula θ = α ≡ sin−1(λ/d), where λ is the wavelength of light and d is the slit width.
Find the total angular width of the central maximum, which is from −α to +α.
Calculate the number of interference fringes within the central maximum using the formula m λ = a sin(θ), where m is the order of the fringe, λ the wavelength of light, and a the separation between the slits.
Count how many integer values of m fit within the range specified by the angles for the central maximum diffraction pattern.
For our specific question, light of wavelength 595 nm passing through slits that are 33 μm wide and 220 μm apart has an interference pattern where the angle θ can be calculated for the first minimum of the single-slit diffraction pattern.
In general, for the whole pattern, the number of bright fringes will greatly depend on the length of the screen and the distance from the slits to the screen, allowing for many fringes outside of the central maximum.