Question

An object is placed 20 cm in front of a concave mirror of focal length 12 cm. Find the position and nature of the image.

Answer 1

Step 1: Given data,

1. Object distance $u=-20cm$(negative sign as the object is placed in front of the mirror)
2. Focal length $f=-12cm$ (focal length taken as negative)

Step 2: Finding the image distance,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ is the mirror formula

By putting the values in the formula, the image distance is given by

$$\begin{gathered} \frac{1}{-12}=\frac{1}{v}-\frac{1}{20} \\ -\frac{1}{12}+\frac{1}{20}=\frac{1}{v} \\ -\frac{2}{60}=\frac{1}{v} \\ -\frac{1}{30}=\frac{1}{v} \\ -30=v \end{gathered}$$

Therefore, the image distance is $-30cm$.

Negative sign of image distance indicates that the image is on the same side as the object.

Step 3: Finding the nature of the image,

Magnification is given by $m=\frac{-v}{u}$

By putting the values of object and image distance,

$$\begin{gathered} m=\frac{-(-30)}{-20} \\ m=-1.5 \end{gathered}$$

Hence, from the value of magnification, it is identified that the image is real and inverted, and magnified. The position of the image is in front of the mirror.