A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm.

Step-by-step solution

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 f - u Case 1: For a real image, m = -2 -2 = -10 -10 - u₁ 20 + 2u₁ = -10 2u₁ = -30 u₁ = -15 cm Case 2: For a virtual image, m = +2 2 = -10 -10 - u₂ -20 - 2u₂ = -10 -2u₂ = 10 u₂ = -5 cm The distance between the two positions of the object is: u = |u₁ - u₂| = |-15 - (-5)| = 10 cm Answer: 10