Question

An object is placed at a distance of 10 cm to left on axis of a convex lens A of focal length 20 cm.Another convex lens of focal length 10 cm is placed co-axially to the right of the lens A at a distance of 5 cm from A. Find the magnification of final image

Answer 1

Here U=-60cm ( distance of object from optical centre considering sign conventions also)

f=+30 cm ( positive for convex lens)

STEP1) Considering first only the image formation by lens :

We have lens formula as -1/u+1/v=1/f

-(1/-60)+1/v=1/30

1/v=1/30–1/60

1/v=1/60

V=60 cm( distance of image formed on the other side of lens)

STEP2)Image formation by mirror

U(distance of object)= 60–10 =50 cm (object is virtual here so real image will be formed by plane mirror)

V(image distance)=50 cm in front of mirror OR 40 cm from optical centre of lens on the other side of lens .

STEP3) image formation by lens again:

U=object distance =+40 cm (object is virtual )

f=+30 cm

V=?

Using lens formula again

-1/40+1/V=1/30

1/v=7/120

V=17.14cm

So finally image is formed at a distance of 17.14 cm from the optical centre of lens on the object’s side .

The distance of image from object is equal to

60–17.14=44.86 cm