The distance between the first- and second-order dark fringes on the screen will be 4.874 × 10⁻⁵ cm.
We have been given monochromatic light with wavelength 590 nm passes through a single slit 2.30 m wide and 1.90 m from a screen,
so λ = 590 nm
d = 2.30 m
D = 1.90 m
We know that the distance between two slits is given as:
Δx = λD / d
Applying values in the above equation we get:
Δx = (590 × 10⁻⁹ m)(1.90 m) / (2.30 m)
= 4.874 × 10⁻⁷ m
= 4.874 × 10⁻⁵ cm
Therefore, the distance between the first- and second-order dark fringes on the screen will be 4.874 × 10⁻⁵ cm.
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