Question

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

Answer 1

1/f = 1/u+1/v

1/15 = 1/(-12) + 1/v

1/v = (5+4)/60

v = 60/9 cm

m = -v/u

m = -60/9 *12

m = 0.55

If object is moved towards the mirror the image will get image distance will get reduced and magnification will increase

Answer 2

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Explanation:

Here,

object size , h1 = 4.5 cm

object distance, u = –12 cm

focal length, f = + 15 cm

image distance , v = ?

magnification, m = ?

As. 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

✴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

⚡As the needle is moved further from the mirror, image moves away from the mirror till it is at focus F of the mirror the size of the image goes on decreasing.