Colour and light

We need to determine the colour and frequency of light with a wavelength of $\lambda =520$ nm = $520\times {10}^{-9}$ m.

We see from [link] that light with wavelengths between 492 - 577 nm is green. 520 nm falls into this range, therefore the colour of the light is green.

We know that

We know $c$ and we are given that $\lambda =520\times {10}^{-9}$ m. So we can substitute in these values and solve for the frequency $f$ . ( NOTE: Don't forget to always change units into S.I. units! 1 nm = $1\times {10}^{-9}$ m.)

The frequency of the green light is $577\times {10}^{12}$ Hz

We need to find the colour and wavelength of light which has a frequency of 490 $\times {10}^{12}$ Hz and which is emitted by the streetlight.

We can see from [link] that orange light has frequencies between 503 - 482 $\times {10}^{12}$ Hz. The light from the streetlight has $f=490\times {10}^{12}$ Hz which fits into this range. Therefore the light must be orange in colour.

We know that

We know $c=3\times {10}^8\mathrm{m}.{\mathrm{s}}^{-1}$ and we are given that $f=490\times {10}^{12}$ Hz. So we can substitute in these values and solve for the wavelength $\lambda$ .

Therefore the orange light has a wavelength of 612 nm.