Final answer:
The type of mirror needed is a concave mirror, as it can produce the required magnified and real image. The object should be placed at a distance of 1 m from the mirror to achieve the desired five times magnification when the image is projected onto a screen 5 m away.
Step-by-step explanation:
The mirror that should be used is a concave mirror. A feature of concave mirrors is that they can produce magnified, upright images when the object is within the focal length. However, this scenario, where the image is to be projected on a screen, implies that the image is real, which means it is inverted. Only concave mirrors can satisfy these conditions, as convex mirrors always produce virtual, erect, and smaller images. For this mirror, the magnification (m) of a mirror is the ratio of the image height (h`) to the object height (h). It is given by the equation m = -v/u.
In this case, the object's height is magnified 5 times, therefore, m = -5. Also, the screen is 5 m (distance of the image from mirror, v) away from the mirror. Substituting these values in our equation for m, we get -5 = -v/u. Which after rearranging gives u = v/5 = 1 m. Which is the distance of the object from the mirror.
Final answer in two lines: A concave mirror is required. The object must be placed 1 m away from the mirror.
Learn more about Concave Mirror