Given focal length of the concave mirror, f=−10 cm.
The image is double the size of the object, so the magnification can be m=±2.
Using the magnification formula in terms of focal length and object distance:
m=f−uf
Case 1: For a real image, m=−2
−2=−10−u1−10
20+2u1=−10
2u1=−30⇒u1=−15 cm
Case 2: For a virtual image, m=+2
2=−10−u2−10
−20−2u2=−10
−2u2=10⇒u2=−5 cm
The distance between the two positions of the object is:
Δu=∣u1−u2∣=∣−15−(−5)∣=10 cm
Answer: 10