Calculate the focal length and nature of a spherical mirror which forms a 1/3 times magnified virtual mage of an object placed 18cm in front of it,

We're having m = 1/3 , and the distance of object from mirror (u) = -18, we has to find the virtual image(v).., focal length(f) and the nature

we know that m = -v/u

1/3 = -v/-18

1/3 = v/18

1*18/3 = v

18/3 = v

6 = v

The image will be made 6 cm away from the mirror behind the mirror

Now Lets find f

1/f = 1/u + 1/v

1/f = 1/-18 + 1/6

1/f = -1+3/18

1/f = 2/18

1/f = 1/9

f = 9

So, the focal length is 9 cm.

The nature of the image is

  • Since the focal length is positive it is a convex mirror.
  • Picture behind the mirror.(right side of cartesian plane)
  • Image is virtual and erect.(Image is always made virtual and erect in Convex mirror)
  • Diminished(shorter than the object)(Image is always dminished by convex mirror)

I calculated v because It is necessary to find where the image will be made.

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