Two concave mirrors of equal focal length f are placed a distance d apart in air. A point source is placed midway between the two mirrors. What should d be so as to get only a single image?
Mirror formula (1/f = 1/u + 1/v)
The Attempt at a Solution
The image distance v1 of the first mirror is calculated using the mirror formula.
1/-f = -2/d + 1/v1
1/v1 = 2/d - 1/f
v1 = df/2f - d
Similarly the image distance v2 of the same object from the second mirror is
v2 = df/2f -d (distances measured from the pole of the second mirror)
The distance of the image formed by the second mirror from the pole of the first mirror is
v3 = d - v2
= d - df/2f -d
= df - d*2 / 2f - d
If the images formed by the two mirrors are to coincide
v1 = v3
df / 2f - d = df - d*2 / 2f - d
This leads to d =0 which is not possible. I would like to know where I have gone wrong. The answer given in the book is 2f and 4f.