Please answer all parts providing detailed explanations or complete calculations. A clear and well-drawn sketch please.
A compelling demonstration of an optical surprise uses a curved mirror to project a real image of a lit bulb (upside down and hidden from class view by a box) on top of a lit bulb (rightside up and on top of the box). *image is attached*
(a) Where do you have to place the box in order to have the image appear right on top of the unlit bulb? The focal length of the mirror is 10 cm. The box with the bulbs is shown at the right in the figure below, ready to be slid to the left to the appropriate position.
(b) How big will the image of the lit bulb be compared to the size of the lit bulb? That is, how big should we make the unlit bulb so that it is the same size as the image of the lit bulb?
(c) On the figure below, sketch the correct position of the lit bulb and draw a ray diagram to confirm your calculation.