Given,

Size of the needle, h = 4.5 cm

Object distance, u = – 12 cm

Focal length of the convex mirror, f = 15 cm

The image distance can be obtained using the mirror equation,

Where,

f is the focal length

u is object distance and

v is the image distance

⇒

⇒

⇒

⇒ v = 6.67 cm

Therefore, the image of the needle is 6.67 cm away

from the mirror.

The magnification is given by

Where,

m is the magnification

h’ is the height of the image

h is the height of the object

v is the image distance

u is the object distance

Using the equation, we get,

⇒

⇒ h' = + 2.5 cm

⇒

⇒ m = 0.56

∴ Magnification is 0.56. And, the height of the image is 2.5 cm. The image is virtual.

If the needle is moved farther from the mirror the image will also move farther away. The size of the image will also decrease gradually.