The thin lens equation
where
is the focal length
is the object distance
is the image distance
only applies to spherical mirrors (or thin lenses) of small aperture. If the mirror has a large aperture, a sharp image is not formed. If a hemispherical mirror is used, a beam of light parallel to the axis intersects on reflection to form a surface called a 'caustic'.
A caustic can often be seen reflected from the surface of tea or coffee in a cup. The caustic in this case is caused when light is reflected from the inside of the cup, which acts as a mirror of large aperture. If light parallel to the principal axis has a small aperture, only those rays close to the principal axis are reflected and the small aperture approximation means theat a sharp image is formed at the point F above, called the principla focus.