For the following object distances and focal lengths of thin

For the following object distances and focal lengths of thin lenses in air, find the image distance and the magnification and state whether the image is real or virtual and erect or inverted. s=40cm, f=20cm s=20cm, f=20cm s=20cm, f=-10cm s=10cm, f=-20cm

Solution

(a).Focal length f = 20 cm

Focal length is positive.So, it is convex lens

Object distance u = 40 cm

From the relation ( 1/v ) -( 1/ u ) = (1/f)

                         (1/v) -( 1/-40) = (1/20)

                         (1/v) = (1/20 ) -(1/40)

                                =(2-1)/40

                                = 1/40

                              v = 40 cm

Magnification m = v /u = 40 cm / -40 cm = -1

So, the image is real ,inverted and in same size.

(b).

Object distance u = 20 cm

From the relation ( 1/v ) -( 1/ u ) = (1/f)

                         (1/v) -( 1/-20) = (1/20)

                         (1/v) = (1/20 ) -(1/20)

                                = 0

                                = 1/0

                              v = infinity

Magnification m = v /u = infinity / -40 cm = infinity

i.e., highly magnified.

So, the image is at inifinity and highly magnified.

(c).

Object distance u = 40 cm

Focal length f = -20 cm

Focal length is negative.So it is concave lens.

From the relation ( 1/v ) -( 1/ u ) = (1/f)

                         (1/v) -( 1/-40) = (1/-20)

                         (1/v) = (1/-20 ) +(1/-40)

                                =(-2-1)/40

                                = -3/40

                              v = -40 /3 = -13.333cm

Magnification m = v /u = -13.333 cm / -40 cm = 1/3

So, the image is erect ,virtual and dimished.

(d).

Object distance u = 20 cm

From the relation ( 1/v ) -( 1/ u ) = (1/f)

                         (1/v) -( 1/-20) = (1/-20)

                         (1/v) = (1/-20 ) +(1/-20)

                                = -2/20

                            v = -10 cm

Magnification m = v /u = -10 / -20 cm = 1/2

So, the image is erect ,virtual and dimished.