A concave lens has focal length of 15 cm. At what distance should an object from the lens be placed so that it forms an image at 10 cm from the lens ? Also, find the magnification of the lens.

Explanation

A concave lens always forms a virtual, erect image on the same side of the object. Image-distance v = –10 cm,
Focal length f = –15 cm,
Object-distance u =?
Since `1/v-1/u=1/f`
or, `1/u=1/v-1/f`
`1/u=1/-10-1/(-15)=-1/10+1/15`
`1/u=(-3+2)/30=1/-30`
or, u = – 30 cm
Thus, the object-distance is 30 cm.
Magnification m = v/u
`m=(-10cm)/(-30cm)=1/3=+0.33`
The positive sign shows that the image is erect and virtual. The image is one-third of the size of the object.