urlregex.js

var pattern = new RegExp('^(https?:\\/\\/)?'+ // protocol
          '((([a-z\\d]([a-z\\d-]*[a-z\\d])*)\\.)+[a-z]{2,}|'+ // domain name
          '((\\d{1,3}\\.){3}\\d{1,3}))'+ // OR ip (v4) address
          '(\\:\\d+)?(\\/[-a-z\\d%_.~+]*)*'+ // port and path
          '([\?\&][\\\/;&a-z\\d%_.~+=-]*)?'+ // query string
          '(\\#[-a-z\\d_]*)?$','i'); // fragment locator

function testString(str){
  if(!pattern.test(str)) {
    return false;
  } else {
    return true;
  }
}

strings = [
  'https://google.com',
  'http://dummyimage.com/600x400/ffffff/000.png',
  'http://dummyimage.com/600x400/ffffff/000.png&text=1',
  'http://www.worldofspectrum.org/showscreen.cgi?screen=1',
  'http://www.worldofspectrum.org/showscreen.cgi?screen=screens.gif',
  'http://www.worldofspectrum.org/showscreen.cgi?screen=screens/in-game/c/ChaseH.Q..gif' 
]

for(var i=0; i < strings.length; i++) {
  string = strings[i]
  result = testString(string)
  console.log(result + ": " + string)
}