Step 1: Recall the wave relation.
For light in vacuum, speed equals wavelength times frequency: $c = \lambda \nu$, so $\nu = \frac{c}{\lambda}$.
Step 2: Note the constants and data.
Here $c = 3 \times 10^8$ m/s and $\lambda = 580$ nm.
Step 3: Convert the wavelength.
$580$ nm $= 580 \times 10^{-9}$ m $= 5.8 \times 10^{-7}$ m.
Step 4: Substitute into the formula.
$\nu = \frac{3 \times 10^8}{5.8 \times 10^{-7}}$.
Step 5: Handle the powers of ten.
Dividing the powers gives $10^{8 - (-7)} = 10^{15}$, so $\nu = \frac{3}{5.8} \times 10^{15}$ Hz.
Step 6: Compute the coefficient.
$\frac{3}{5.8} \approx 0.517$, giving $\nu = 0.517 \times 10^{15} = 5.17 \times 10^{14}$ Hz.
Step 7: Match the option.
The frequency is $5.17 \times 10^{14}$ Hz, which is option (3).
\[ \boxed{\nu = \dfrac{3 \times 10^8}{5.8 \times 10^{-7}} = 5.17 \times 10^{14}\ \text{Hz}} \]