The mirror here definitely will be concave as only concave mirror can form a sharp image on a screen and we know that both plane and convex mirror form virtual image which can not be obtained on screen.
Since the image is sharp, that means it will be formed at focus and the image is formed at focus only when object is at infinity. So we can say that the screen must be kept at focus to obtain the image. So, the distance between screen and mirror is equal to the focal length of the mirror.