A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature, position and size of the image formed.
Solution
Distance of the object from the mirror 'u' = −9cm
Height of the object 'ho' = 2 cm
Focal length of the mirror 'f' = −4 cm
We have to find the distance of the image 'v' and height of the image 'hi'.
Using the mirror formula, we get
`1/f=1/v+1/u`
`1/-4=1/v+1/-9`
`1/-4=1/v-1/9`
`1/9-1/4=1/v`
`(4-9)/36=1/v`
`-5/36=1/v=(-1)/7.2`
v=7.2 cm
Therefore, distance of the image 'v' is 7.2 cm.
Now, using the magnification formula, we get
`m=h_i/h_o=-v/u`
`h_i/H_o=-((-7.2))/-9`
`h_i/2=((-7.2))/-9`
`h_-i=(2xx(-7.2))/9`
`h_i=-1.6 cm`
Thus, the height of the image 'hi' is 1.6 cm.
Again, using the magnification formula, we get
`m=-v/u`
`m=-(-7.2)/-9`
m=-0.8
Thus, the image is real, inverted and small in size.
