Is it normal for dental implants to be shorter than normal teeth? (photo)

Hi there,
Your implants and crowns are there for 2 reasons...esthetics and function. You have to be able to chew on the implant crowns. The implant crowns should lightly touch the teeth in the opposing upper jaw. 
I would have your dentist check it. You should be able to bite and hold the thickness of a piece of paper on all your teeth with the bite slightly lighter on the implant crowns as there is no periodontal ligament around the implant to absorb shock. 
In the photo, it appears that the bite is so open that you cannot grab a piece of cardboard. 
Have your dentist balance your bite so you do not overload the function on your other teeth.
Best regards,
Dr. Ed Lowe

now a days many dentists do this, just to prevent lateral forces on implant for long life of implant. but it is not advisable and that results in undesirable forces in TMJ. perfect ideal occlusion is must.

You must have an excellent occlusion no matter what. Your teeth must touch otherwise you may develope TMJ problems