Question

A concave mirror of focal length \(10\,\text{cm}\) 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.

Answer 1

Correct Answer: 30

Step 1: Understanding the Question:
A concave mirror can form a double-sized image in two cases: real (inverted) and virtual (erect). We need to find the distance between these two object locations.
Step 2: Key Formula or Approach:
Magnification formula: \(m = \frac{f}{f - u}\).
Step 3: Detailed Explanation:
Given \(f = -10 \text{ cm}\). Image is double sized, so \(|m| = 2\).
1. Case 1: Real image (\(m = -2\)):
\[ -2 = \frac{-10}{-10 - u_1} \Rightarrow 20 + 2u_1 = -10 \Rightarrow 2u_1 = -30 \Rightarrow u_1 = -15 \text{ cm} \]
2. Case 2: Virtual image (\(m = +2\)):
\[ 2 = \frac{-10}{-10 - u_2} \Rightarrow -20 - 2u_2 = -10 \Rightarrow 2u_2 = -10 \Rightarrow u_2 = -5 \text{ cm} \]
3. Distance between positions \(= |u_1 - u_2| = |(-15) - (-5)| = 10 \text{ cm}\).
Step 4: Final Answer:
The distance between the two object positions is 10 cm.