Which of the following correctly describes the image of an object, \(4 cm\) from a diverging lens of focal length\(12 cm\) ?
A. The image is virtual, \(3 cm\) in front of the lens B. The image is real, \(6 cm\) bchind the lens C. the image is virtual, \(6 cm\) in front of the lens D. The image is real, \(3 cm\) in front of the lens
Correct Answer: A
Explanation
Focal length of diverging lens is -ve i.e. \(f=-12 cm , u=4 cm\) $$ \begin{aligned} \frac{1}{f} &=\frac{1}{v}+\frac{1}{u} \\ \frac{-1}{12} &=\frac{1}{v}+\frac{1}{4} \\ \frac{1}{v} &=\frac{-1}{12}-\frac{1}{4} \\ \frac{1}{u} &=\frac{-3-1}{12} \\ v &=\frac{12}{-4}=-3 cm \end{aligned} $$ i.e. \(3 cm\) in front of the lens
