"If we place two concave both of focal length f mirrors at a distance d facing each other and let source S be midway between so what should be the value of d so that only one image is formed" I have tackling this problem for half an hour now and I got till here: let the first light be hit to mirror 1 on the right the focal length =-f and object distance(u) =-d then image distance(v)=fd/(-d+2f) that the easy part
So if we place object between the pole and focus then image will be virtual
And if we place the object at centre of curvature the image will be formed at centre of curvature
I think placing it between the focus and centre of curvature will result in multiple reflection which is not allowed
Then the object in the middle forms an image at the same place. And that image than acts as the object for the second mirror and it also forms an image in the same place.
So you do get multiple reflections, but all the images are at the same place.
Then the light from the object hits the first mirror, and because the object is at f the rays reflecting from the first mirror are parallel so no image is formed by the first mirror. OK so far?
Then the parallel rays hit the second mirror, and they form an image at the focal point of the second mirror i.e. at the same place as the original object.
So again the object and image coincide, but this time the two reflections produced only a single image.
So I guess the question just means that the images have to be in the same place as the object, and it doesn't matter how many images are formed as long as they are all in the same place.