Final answer:
To find the number of bright interference fringes in the whole pattern for light passing through a double-slit, we use the interference formula and the given dimensions. We calculate that there are approximately 693 bright interference fringes in the whole pattern.
Step-by-step explanation:
To determine the number of bright interference fringes in the entire pattern for light passing through a double-slit, we can use the principles of interference and the formula for the condition of maxima (bright fringes):
d sin(θ) = mλ
Where d is the slit separation, θ is the angle of the fringe from the centerline, m is the order of maximum, and λ is the wavelength of the light.
Since the question doesn't specify the distance to the screen or the width of the entire pattern, we'll work with the assumption that the entire pattern is visible on a screen that's sufficiently large and far enough away.
For the first-order maximum (m=1), the angle θ can be small and sin(θ) ≈ θ for small angles (θ in radians). The angle cannot exceed ±90 degrees (or ±π/2 radians), hence a fringe will only be observed if the angle by which the light is diffracted fits within this range.
Given d = 225 µm and λ = 650 nm (which is 650 x 10-9 m), let's convert the unit of d to match λ by turning micrometers into meters (1 µm = 1 x 10-6 m):
d = 225 x 10-6 m
To find the maximum possible m value (the order of the bright fringe), rearrange the formula and substitute θ for the extreme case of 90 degrees:
m = d / λ
Substituting the known values:
m = (225 x 10-6) / (650 x 10-9) ≈ 346.15
Since m must be an integer, the maximum number of interference fringes on one side of the central maximum is 346. Due to symmetry, the total number of bright fringes in the whole pattern would be doubled, plus the central bright fringe:
Total = 2m + 1 = 693
Thus, there would be approximately 693 bright interference fringes in the whole pattern.