Question

An object is placed \(30\,\text{cm}\) in front of a concave mirror of focal length \(20\,\text{cm}\). The image distance is

• A. \(-60\,\text{cm}\)
• B. \(+60\,\text{cm}\)
• C. \(+30\,\text{cm}\)
• D. \(-30\,\text{cm}\)

Hint:

Mirror formula: \[ \boxed{\frac{1}{f}=\frac{1}{v}+\frac{1}{u}} \] For a concave mirror: \[ f<0 \] Real image: \[ v<0 \] Virtual image: \[ v>0 \] Always follow the New Cartesian Sign Convention.

Answer 1

The Correct Option is A

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

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

Step 3: Identify the correct option. \[ \boxed{v=-60\,\text{cm}} \] The negative sign indicates that the image is real and formed in front of the mirror. Therefore, \[ \boxed{\text{(A)}} \] is the correct answer.