The image formed by a spherical mirror is real, inverted and is of magnification -2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.

#### Solution

Given: Magnification, m = -2

Distance of the image, v = -30 cm

Magnification, `m=-v/u`

∴`u=-v/m=-((-30))/((-2))`

∴u = -15 cm

Substituting these values in the mirror formula

`1/f=1/v+1/u`

=`1/((-30))+1/((-15))`

`1/f=-1/10`

∴f = 10 cm

When the object is moved 10 cm towards the mirror the new position of the object is

u' = -(15-10) = 5 cm

Substituting the new value in the mirror formula

`1/f=1/v+1/u`

`1/v^'=1/f-1/u=1/10-1/((-5))`

`1/v^'=1/10`

∴v' = 10 cm

Thus, the image is located 10 cm behind the mirror.

And magnification,`m'=(v')/(u')=-10/((-5))`

m' = 2

Since magnification is positive the image is erect and virtual.

Thus, the image is erect,virtual and magnified in nature.