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

Step 2 -

v can be found using the mirror formula

1/u + 1/v = 1/f

1/v = 1/f - 1/u ….. (1)

Where u is the object distance

v is the image distance

f is the focal length

Magnification m = h2/h1 = -v/u ….. (2)

Where h1 is the height of the object

h2 is the size of the image

Step 3- Now we have to find the Image distance:

We have u = -12 cm and f = +15 cm

Substitute the values in equation (1) we get

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

= (4 + 5)/60

On simplifying we get

= 9/60

v = 60/9 = 6.7 cm

Consequently, the needle's image is 6.7 cm away from the mirror. It's also on the opposite side of the mirror.

Image size:

The size of the image is given by the magnification formula:

6.7 cm of the convex mirror is used to form the image. It has to be erect and virtual.

if h2 is the size of the image, then

m = h2/h1 = -v/u

m = -6.7/(-12) = 0.558

h2/h1 = 0.558

h2 = 0.558 x 4.5

In simplification we get

h2 = 2.5 cm

Magnification m = h2/h1 = 2.5/4.5 = 0.56

The picture will gradually get smaller and move farther away from the mirror if the needle is moved in that direction.

• Image distance v = 6.7 cm away from the mirror.
• Image size h2 = 2.5 cm
• The picture will progressively get smaller and move away from the mirror when the needle is positioned further away from it.

Summary:

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

A convex mirror with a 15 cm focal length is 12 cm away from a 4.5 cm needle. The other side's picture is 6.7 cm from the mirror, the magnification is 0.558, and if the needle moves further away from the mirror, the image will recede and the side will be shrunk.