A convex mirror having a radius of curvature of 30cm is fixed at one end of a long corridor. A student stands on the principal axis at a distance of 50cm from the mirror.
(i) Determine the focal length of the mirror with the correct sign.
(ii) Calculate the position of the image of the student with respect to the mirror.
(iii) Compute the magnification produced and state how the size and nature of the image compare with those of the student.