Two lenses of powers +4 D and -14 D form a combination.If a 2 cm size object is placed 30 cm from this combination,find the position,nature and size of the image.

Explanation

`P_(1)=+4D, P_(2)=-14 D`
Power of combination of lenses `=P=P_(1)+P_(2)`
`P=4-14=-10D`
Let f=Focal length of combination of lenses
`f=1/P=1/(-10)=-0.1m`
`f=-10cm`
`u=-30cm`
`v=?`
By lens formula
`1/v 1/v-1/u=1/f`
`1/v-1/(-30)=1/(-10)`
`1v+1/30=-1/10`
`1/v=-1/10-1/30=(-3-1)/30`
`=(-4)/30=-2/15`
`impliesv=-15/2cm=-7.5cm`
Size of the object `=O=+2cm`
Magnification `m=v/u=I/O`
Size of image `(I)=v/u(O)=-7.5/(-30)(2)`
`=0.5m`
Image formed is virtual, erect and smaller in size than object.