Height of the needle, h1 = 4.5 cm
Object distance, u = −12 cm
Focal length of the convex mirror, f = 15 cm
Image distance = v
The value of v can be obtained using the mirror formula
1/u + 1/v = 1/f
1/v = 1/f – 1/u
putting u = –12 cm and f = +15cm , we get
1/v = 1/15 – 1/-12 = 4+5/60 = 9/60
v = 60/9 = 6.7 cm
Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.
The image size is given by the magnification formula:
image is formed 6.7 CM behind the convex mirror. it must be virtual and erect.
if h2 is size of image , then m = h2/h1 = -v/u
m = h2/h1 = –(6.7)/–12 = 0.558
h2 = 0.558
h1 = 0.558 * 4.5 = 2.5 cm
Hence magnification m = h2/h1 = 2.5/4.5 = 0.56
If the needle is moved farther from the mirror, the image will also move away from the mirror, and the size of the image will reduce gradually.