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Answer:
λ = 5.85 x 10⁻⁷ m = 585 nm
f = 5.13 x 10¹⁴ Hz
Explanation:
We will use Young's Double Slit Experiment's Formula here:
[tex]Y = \frac{\lambda L}{d}\\\\\lambda = \frac{Yd}{L}[/tex]
where,
λ = wavelength = ?
Y = Fringe Spacing = 6.5 cm = 0.065 m
d = slit separation = 0.048 mm = 4.8 x 10⁻⁵ m
L = screen distance = 5 m
Therefore,
[tex]\lambda = \frac{(0.065\ m)(4.8\ x\ 10^{-5}\ m)}{5\ m}[/tex]
λ = 5.85 x 10⁻⁷ m = 585 nm
Now, the frequency can be given as:
[tex]f = \frac{c}{\lambda}[/tex]
where,
f = frequency = ?
c = speed of light = 3 x 10⁸ m/s
Therefore,
[tex]f = \frac{3\ x\ 10^8\ m/s}{5.85\ x\ 10^{-7}\ m}\\\\[/tex]
f = 5.13 x 10¹⁴ Hz