A 4.5 CM needle is placed at 12 cm away from a convex mirror of focal length of 15cm. Give the location of the image and the magnification. Describe what happened as the needle is moved further from the mirror.

Convex mirror is also known as diverging mirror because it diverges the rays of light, which fall on its reflecting surface. Convex Mirror is a curved mirror where the reflective surface bulges out towards the light source. This bulging out surface reflects light outwards and is not used to focus light. There are two possibilities related to the position of the object in a convex mirror.

• When the object is at infinity
• When an object is between infinity and pole

Given

• 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

Now putting the values in the above equation

• u = –12 cm
• f = +15cm

1/v = 1/15 – 1/-12

1/v = 4+5/60

1/v = 9/60

v = 60/9

v = 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.

Image size

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

or,

m = h2/h1

m = –(6.7)/–12

m = 0.558

h2 = 0.558

h1 = 0.558 × 4.5

h1 = 2.5 cm

Hence magnification m = h2/h1

m = 2.5/4.5

m = 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.