Tangible Augmented Reality (AR) interfaces use physical objects as a medium for interacting with virtual objects. In many cases, they track physical objects using computer vision techniques to attach corresponding virtual objects on them. However, when a user tries to have a closer look at the virtual content, the tracking can fail as the viewpoint gets too close to the physical object. To prevent this, we propose an automatic zooming method that helps users to achieve a closer view to the scene without losing tracking. By updating the zoom factor based on the distance between the viewpoint and the target object, a natural and intuitive zooming interaction is achieved. In a user study evaluating the technique, we found that the proposed method is not only effective but also easy and natural to use.