If a concave mirror has a focal length of 10 cm, find the two positions where an object can be placed to give, in each case, an image twice the height of the object.
Solution
Given,
Focal length (f) of the concave mirror = -10 cm
Case-1
The image is real, and its magnification (m) is -2.
Using the magnification formula, we get
`1-10=12u+1u`
`m=(-v)/u`
`-2=(-v)/u`
v=2u
Now, using the mirror formula, we get
`1/f=1/v+1/u`
`1/-10=1/2u+1/u`
`1/-10=1/(2u)+2/(2u)=3/2u`
`u=(3xx(-10))/2=-15 cm
The object should be placed at a distance of 15cm from the concave mirror.
Case-2
The image is virtual and has a magnification 'm' of 2.
Using the magnification formula, we get
`m=-v/u`
`2=-v/u`
v=-2u
Now, using the mirror formula, we get
`1/f=1/v+1/u`
`1/-10=1/(-2u)+1/u`
`1/-10=-1/(2u)+2/(2u)=1/(2u)`
`u=(-10)/2=-5 cm `
Thus, the object should be placed at a distance of 5 cm in front of the concave mirror.
