Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency $1.20\times 10^{15}\text{ Hz}$?

Video Transcript

This is College Physics Answers with Shaun Dychko. We want to know what size is the smallest observable detail using a microscope that uses ultraviolet light with a frequency of 1.20 times 10 to the 15 hertz? So the smallest observable detail will be about the size of the wavelength of this light and so the question is then what's the wavelength of this light? So the speed of light is frequency multiplied by the wavelength then we can solve for λ by dividing both sides by frequency. So the wavelength then which is the size of the smallest observable detail is 2.998 times 10 to the 8 meters per second divided by 1.20 times 10 to the 15 hertz and that is about 0.250 micrometers.