Question

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 farther from the mirror.​

Answer 1

Answer:

THE IMAGE BECOMES SMALLER AS IT GOES FARTHER.

Answer 2

Solution

Given :-

• h' = 4.5 cm
• u = - 12 cm
• f = 15 cm

Find :-

• Location and magnification of image

Explanation

Using Mirror Formula

$\boxed{\underline{\tt{\red{\:\dfrac{1}{f}\:=\:\dfrac{1}{u}\:+\:\dfrac{1}{v}}}}}$

keep all above Values

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

==> 1/v = 1/15 + 1/12

==> 1/v = (4+ 5)/60

==> 1/v = 9/60

==> v = 60/9

==> v = 20/3

==> v = 6.6 cm

Now, Calculate magnification

Using Formula

$\boxed{\underline{\tt{\green{\:m\:=\:\dfrac{h"}{h'}\:=\:\dfrac{-v}{u}}}}}$

Keep all above Values,

==> h" = (-v × h' )/u

==> h" = -(6.6 × 4.5)/(-12)

==> h" = + 2.5 cm

Hence, Magnification of image

==> m = h"/h'

keep values,

==> m = 2.5/4.5

==> m = 25/45

==> m = 0.56

Since

• Height of image is 2.5 cm. The positive sign indicate image is virtual & diminished .

____________________