Mathematically, in triangle abc, side bc is the opposite of angle bac, & thus length of bc depends on angle bac. In abc & ade, bac = dae, (Reciprocal angle). abc = aed (As bc||de & be intersects them, they are alternate angles) acb = ade (As bc||de & cd intersects them, they are alternate angles) Therefore, abc & ade are similar triangles & thus bc/de = ab/ae = ac/ad = k (some constant). Since, bc/de = k, => bc = k*de which implies that bc de (bc is proportional to de). This relation implies that, the field of view is proportional to the size of the sensor used in camera. Field of view also depends on the focal length of the lens.
The above diagram shows that the Field of view is inversely proportional to the Focal Length of the lens used in a camera. Camera phones generally use sensor sizes in the range of ~1/4 to 2/3. The problem of fitting a large sensor in a mobile device isnt only about the sensor itself, the greater challenge is the fact that the larger the sensor, the larger the lens need to be. This is because larger sensors require one to get closer to their subject, or to use a longer focal length to fill the frame with that subject. So, to increase the field of view, we cant enlarge the camera sensor as we wish or cant decrease the focal length of the lens. And thats why the field of view of smartphone camera/digital camera is smaller comparing to the field of view of human eyes.