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.

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 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

or,

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.

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