question_answer

A 0.5 cm high object is placed at 30 cm from a convex mirror whose focal length is 20 cm. Find the position and size of the image.

A) 12 cm, 0.2 cm

B) 18 cm, 0.2 cm

C) 6 cm, 0.5 cm

D) 5 cm, 0.1 cm

Correct Answer: A

Solution :

[a]

Here, Object distance, \[u=-\text{ }30cm\]

Focal length, \[f=+20\text{ }cm\]

We know, mirror formula, \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\] \[\Rightarrow \]   \[v=\frac{uf}{u-f}=\frac{-30\times 20}{-30-20}=+12\,cm\]

Again, magnification, \[m=\frac{-v}{u-f}=\frac{-12\,cm}{30\,cm}=\frac{2}{5}\]

Now, Image height \[=m\times \] object height \[=\frac{2}{5}\times 0.5\,cm=0.2\,cm\]

Thus the image is formed behind the mirror at a distance of 12 cm from the pole. Image height is 0.2 cm.