9.9 An object of size 3.0cm is placed 14cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

Hint: \(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

Step 1: Find the position of the final image.
Object distance, u = -14 cm
Focal length of the concave lens, f = -21 cm
Using the lens formula:

1v-1u=1f
1v=1f+1u
1v=121-114=-2-342=-542
v=-425=-8.4 cm

The image is formed 8.4 cm away from the lens on the right side. The negative sign shows that the image is erect and virtual. 

Step 2: Find the magnification of the image.
The magnification of the image:

m=Image height h2Object height h1=vu
h2=-8.4-14×3=1.8 cm.
Hence, the height of the image is 1.8 cm.
If the object moves further away from the lens, then the virtual image will move towards the focus of the lens, but not beyond it. The size of the image will decrease with the increase in the object distance.