Question

An object is placed 10 cm in front of a concave mirror with a focal length of 20 cm. What is the magnification produced?

• A. 1
• B. 2
• C. 0.5
• D. -2

Hint:

Use the mirror formula \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \) and the magnification formula \( m = -\frac{v}{u} \) carefully. Pay attention to sign conventions!

Answer 1

The Correct Option is B

Given: \[ f = -20\, \text{cm}, \quad u = -10\, \text{cm} \] Using the mirror formula: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \Rightarrow \frac{1}{-20} = \frac{1}{v} + \frac{1}{-10} \Rightarrow \frac{1}{v} = \frac{-1}{20} + \frac{1}{10} = \frac{1}{20} \Rightarrow v = 20\, \text{cm} \] Now, magnification is: \[ m = -\frac{v}{u} = -\frac{+20}{-10} = +2 \] This means the image is virtual, upright, and magnified by a factor of 2.