Question:
A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take L << |v-f|
Solution:
The mirror formula is
1/v + 1/u = 1/f
u is the object distance
v is the image distance
du = |u1 – u2| = L
Differentiating on the both sides we get,
dv/v2 = -du/u2
v/u = f/u-f
du = L, therefore, image length is f2/(u-f)2L