Question

a 4.5 cm needle is placed 12 CM away from a convex mirror of focal length 15 cm give the locations of the image and magnification describe what happened to the image as the needle is move further from the mirror
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Answer 1

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/f = 1/v - 1/u

1/u = 1/v - 1/f

= 1/-25 - 1/5

= -5 -1/25

= -6/25

u = -25/6 = -4.167 cm

1/v = 1/f - 1/u

1/f = 1/u + 1/v

= 1/15 + 1/12

= 4 +5/60

= 9/60

f = 60/9 = 6.7 cm

The image size is

m = h2/h1 = -v/u

h2 = -v x h1 /u

= -6.7 x 4.5/ -12 = 2.5 cm

Hence Hence, magnification of the image, m = h2/h1 = 2.5/4.5 = 0.56


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Answer 2

Given: A 4.5cm needle is placed 12cm away from a convex mirror of focal length 15cm.

To find the location of the image and the magnification.  

Solution:

According to the given criteria,

Object height, ho=4.5cm

Object distance, u=−12cm

Focal length of the mirror, f=15cm

Applying mirror formula, we get

f1=v1+u1⟹151=v1+−121⟹v1=151+121⟹v1=604+5⟹v=6.6cm

Hence, the image is at a distance of 6.6 cm,

Magnification, m=−uv=hiho⟹−−126.6=hi4.5⟹hi=6.64.5