# 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.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

A 4.5 cm needle is placed 12 cm away from a convex mirror of a focal length of 15 cm. The image is 6.7 cm away from the mirror on the other side, the magnification is 0.558 and if the needle moves farther from the mirror, the image will move away and the side will be reduced. Steps to know the location of the image and the magnification:

Step 1 – It is given that,

The focal length of the convex mirror f = 15 cm

Height of the needle h1 = 4.5 cm

Distance of object u = -12 cm

Let the distance of the image = v

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.

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