Question

Two thin lenses with focal lengths of magnitude 18.0 cm, the first diverging and the second converging, are placed 11.00 cm apart. An object 3.70 mm tall is placed 4.75 cm to the left of the first (diverging) lens.

(a) Where is the image formed by the first lens located?

(b) How far from the object is the final image formed?

(c) Is the final image real or virtual?

(d) What is the height of the final image?

(e) Draw a principal-ray diagram for this situation.

Answer 1

Focal length of combination can be given as :

1/f = 1/f₁ + 1/f₂ - d/(f₁.f₂)

f₁= -18 cm, f₂=+18 cm

1/f = 1/(-18) + 1/18 - 11/(-18.18)

f = 29.45 cm

distance of final image from first lens ,

v= u.f/(u-f)= (4.75)(29.45)/(4.75-29.45) = -5.663

v is negative so image is virtual

Magnification = -v/u = 1.19

Height of final image h = 1.19×3.70=4.403 mm