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.