How to handle media query for responsive design for IE8 ?

Mobile devices do not use IE8 so IE8 is most likely to be used with large enough screens which will use the default css. But if you care to make IE8 work with media queries you can try this:https://github.com/scottjehl/Respond

If you care about the mobile version of IE you can can use IE conditional comments:

https://blogs.msdn.com/b/iemobile/archive/2010/12/08/targeting-mobile-optimized-css-at-windows-phone-7.aspx?Redirected=true