An object is placed (a) 20 cm, (b) 4 cm, in front of a concave mirror of focal length 12 cm. Find the nature and position of the image formed in each case.
Solution
Case (a)
Distance of the object from the mirror (u) = -20 cm
The focal length of the concave mirror (f) = -12 cm
We have to find the distance of the image (v).
Using the magnification formula, we get
`1/f=1/v+1/u`
so
`or 1/-12=1/v+1/-20`
`1/-12=1/v-1/20`
`or 1/20-1/12=1/v`
`or(3-5)/60=1/v`
`or -2/60=1/v`
`or v= 60/-2`
`v=-30` cm
The image will be at a distace of 30 cm in front of mirror.Again,
Magnification `(m)=(-v)/u `
`m=-(-30)/-20=-1.5`
Therefore, the image will be real, inverted and enlarged.
Thus the image is real, inverted and enlarged.
Case B
Distance of the object from the mirror (u) = -4 cm
The focal length of the concave mirror (f) = -12 cm
We have to find the distance of the image (v).
Using the mirror formula, we get
`1/f=1/v+1/u`
`1/-12=1/v+1/-4`
`or 1/4-1/12=1/v`
`or(3-1)/12=1/v`
`or 2/12=1/v`
Therefore, distance of image (v) is 6 cm.Now, using the magnification formula, we get
`m=-v/u`
`m=-6/-4=1.5`
Thus, the image is virtual and erect.
