A person of height \(H\) stands a distance \(d\) in front of a flat, vertical plane mirror mounted on a wall. The person can see their entire body (from the top of the head to the bottom of the feet) in a mirror of minimum vertical length \(L_{\text{min}}\). The person then steps backward so that their distance from the mirror increases to \(2d\). Which of the following correctly pairs the new minimum vertical mirror length required for the person to see their entire body with the change in the angular size of the image subtended at the person's eyes?