Question
Draw a ray diagram to show the formation of the image of an object placed between f and 2f of a thin concave lens. Deduce the relation between the object distance, the image distance and the focal length of the lens under this condition.
Solution
Derivation of lens formula for a concave lens:
The ray diagram for the formation of image of an object which is placed between F1 and 2F1 of a thin concave lens is shown in Fig.
The image A'B' formed is virtual and erect.
are similar,
...(1)
are similar,
But MO = AB,
...(2)
From (1) and (2), we get
According to new cartesian sign convention,
Object distance, OB = -u
Image distance, OB' = -v
Focal length, OF = -f
Relation between u,v anf f can be established as follows:
Dividing both sides by uvf, we get
which is the required relation between u, v and f for a concave lens.
The ray diagram for the formation of image of an object which is placed between F1 and 2F1 of a thin concave lens is shown in Fig.
The image A'B' formed is virtual and erect.
are similar,
...(1)
are similar,
But MO = AB,
...(2)
From (1) and (2), we get
According to new cartesian sign convention,
Object distance, OB = -u
Image distance, OB' = -v
Focal length, OF = -f
Relation between u,v anf f can be established as follows:
Dividing both sides by uvf, we get
which is the required relation between u, v and f for a concave lens.
