Question

The focal length of a concave mirror is \(20\text{ cm}\). If the object is placed at \(30\text{ cm}\) from the mirror, the image distance will be:

• A. \(60\text{ cm}\)
• B. \(30\text{ cm}\)
• C. \(12\text{ cm}\)
• D. \(24\text{ cm}\)

Hint:

Remember sign convention: \[ f<0,\quad u<0 \] for concave mirrors.

Answer 1

The Correct Option is A

Step 1: Use mirror formula. \[ \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \] Given: \[ f=-20\text{ cm}, \qquad u=-30\text{ cm} \]

Step 2: Substitute values. \[ \frac{1}{-20} = \frac{1}{v} + \frac{1}{-30} \] \[ \frac{1}{v} = -\frac{1}{20} +\frac{1}{30} \] \[ \frac{1}{v} = \frac{-3+2}{60} = -\frac{1}{60} \] Thus: \[ v=-60\text{ cm} \] Magnitude: \[ \boxed{60\text{ cm}} \]