As shown in the figure, a point source S is positioned midway between two converging mirrors having equal focal length f . Determine the values of d for which only a single image is formed.

Step-by-step solution

For a single image to be formed, the images produced by both mirrors must coincide. Let the distance between the mirrors be d . The point source S is placed midway, so the object distance for each mirror is u = - d 2 . Using the mirror formula for one of the concave mirrors (with focal length F = -f ): 1 v + 1 u = 1 F 1 v - 2 d = - 1 f 1 v = 2 d - 1 f = 2f - d df v = - df d - 2f The negative sign indicates the image is formed at a distance df d - 2f in front of the mirror. By symmetry, the second mirror forms its i