Responsive theme and image size

I am not new to website design, did 14 years doing brochure types.Now just starting with WP and trying out various plugins before finding new clients.

I want to specialise in designs for mobile devices, therefore I only need to use images that have enough resolution to look good on that size of device. The problem is if my website is viewed on a 17 inch or larger the images look fuzzy.

Is there a way to get the theme to select a low resolution (small) image for one size of screen and a high resolution (lsrge) image for larger screens, on the fly, and without me having to use any code? Or is my question redundant because themes do the compression automatically? I ask because I just don’t know enough about the technology of PHP, maybe what I have is normal.

My site is not what I call polished so please no derogative comments. Have a look at the header image on a phone and it is good, then look on a largish laptop or bigger and the header looks poor. The picture is 1200 pix wide.

Thanks Greg