How to to write the loop using JavaScript?

Something like the following, but without the photos variable i added to simplify things.

var photos = [
{
link: "a.html"
}, {
link: "b.html"
}
];

photoHTML = "";
for (i = 0; i < photos.length; i++) {
    var photo = photos[i];

      photoHTML += '<a href="' + photo.link + '" class="image" target="_blank">';
}
console.log(photoHTML);

from code I don't see many stuff: the loop is well done but maybe the problem is within the code that isn't visible in the post. I have tried to figure what you want really do.

photoHTML="<ul>";
 for (i = 0; i < photo.length; i++) {
      photoHTML += '<li class="grid-25 tablet-grid-50">';
      photoHTML += '<a href="' + photo.link + '" class="image" target="_blank">';
      photoHTML += '<img src="' + photo.media.m +'"></a></li>';
  }
photoHTML+="</ul>";

I hope that I have helped you

We'd need to see more of your code. Based on what you published, I suspect that it has to do with the photos variable not being populated with the JSON object. With the way that the jQuery each function is setup, this is automatic. I suspect that your program doesn't know that "photo" is an item in the API's "items" array.